Angular Sum Research Articles

Application of residual network based on multispectral attention mechanism in stepped eddy current thermography defect detection

The stepped eddy current thermography nondestructive testing technique has a low and uneven temperature rise under weak excitation conditions, which brings great challenges to the quantitative analysis of defects in the inner wall of pressure vessels. To solve the above problems, this paper proposes a multi-spectral channel attention residual network model based on a Gramian angular difference field (GADF) for automatic detection and quantification. Firstly, the noise reduction and compression of temperature time series data are accomplished by singular value decomposition and piecewise aggregate approximation. Secondly, three infrared feature strategies commonly used for quantitative analysis were transformed by GADF and Gramian angular sum field (GASF) techniques to filter out the infrared feature data sets that contain the most defective feature information. Finally, the frequency domainization of the feature map is realized by embedding the multispectral channel attention in the residual network. The global dependencies and relevant essential features of infrared data are effectively captured, and the redundant feature information generated by deep learning feature maps is suppressed. The effectiveness of the model is verified by comparing several time-series models with advanced deep-learning models. The results show that the proposed model has excellent performance in terms of accuracy, stability, and generalization ability. Meanwhile, the model can effectively extract the defects in the region of uneven temperature rise.

An intelligent Island detection scheme to enhance grid resilience

The importance of strengthening grid resilience has grown with the increase in environmental destruction and modern power grid complexity, as a consequence of power outages inflicted by human intrusion and extreme weather events. Micro-grids (MGs) have proven to be a viable alternative in such circumstances. However, these occurrences are highly unpredictable, resulting in unintended islands of MGs with negative consequences. As a response, alerting its distributed generations about unintended island is indeed a crucial issue for enhancing grid resilience with MG. Therefore, it is essential to develop a technique for the efficient and accurate detection of unintended islands. There has been an increase in the use of micro-phasor measurement units (µ-PMUs) in MG. In the perspective of this, using an efficient µ-PMU, the research provides a method for finding unintended islands in a MG. The µ-PMU analyses the solar generator bus voltage and analyzes it with symmetrical components for island identification. This study introduces a µ-PMU based Fortescue-transform and random forest algorithm method for rapid detection of unintended islanding in distribution generation system. The approach monitors voltage phasor of zero and negative sequence, calculating angular sum over time to distinguish islanding event from other disturbance. Using Matlab/Simulink, the proposed method is evaluated on the IEEE-34 node distribution network. Multiple simulations provide validation for the method’s resilient performance. The methodology proposed has a detection time of 20 ms.

An island detection methodology with protection against cyber attack

Unplanned islanding of micro-grids is a significant barrier to supplying continuous power to key customers. The identification of the islanding moments must be rapid to enable the distributed generators (DG) to perform control measures in the shortest possible period. Micro phasor measuring units (µ-PMU) are gaining popularity in distribution systems and micro grids as a result of their ability to produce high-quality data at a high speed. These µ-PMUs can be utilized to detect islands. However, the µ-PMU relies heavily on the communication system for transmission of data, which is vulnerable to cyberattacks. In consideration of the previous technique, this research provides a smart island detection application with µ-PMU having lowered cyberattack probabilities. This representation is equipped with a µ-PMU implemented on the relevant DG’s bus. The voltage data acquired from these µ-PMUs are processed using the sequence transformation in order to simulate the sequence component angle. The angular sum of the negative and positive sequence components is evaluated and the maximum value is deployed for detection of islanding. MATLAB/Simulink tests the proposed approach through an IEEE-34 node distribution network. Multiple simulations demonstrate the robustness of the technique.

Bearing fault diagnosis method based on the Gramian angular field and an SE-ResNeXt50 transfer learning model

Fault diagnosis methods for rolling bearings based on deep learning have become a research hotspot. However, these methods mostly use convolutional neural networks (CNNs), which have the problem of gradient dispersion or disappearance as the network deepens. Moreover, directly converting vibration signals into images as network input cannot preserve the temporal correlation between signals. In the case of small datasets and complex and variable working conditions, the accuracy of fault diagnosis is low and the generalisation ability is poor. To solve the above problems, a rolling bearing fault diagnosis method based on the Gramian angular field (GAF) and an SE-ResNeXt50 transfer learning model is proposed. Firstly, the parameters of the GAF obtained from multiple experiments are selected and the one-dimensional time-series vibration signal is encoded by combining the data enhancement method, and converted into a Gramian angular difference field (GADF) diagram and a Gramian angular sum field (GASF) diagram with local time information and uniqueness. Then, a fine-tuning transfer learning strategy is used to transfer the pre-trained model parameters to an SE-ResNeXt50 model, which improves the training speed of the model and improves the overfitting problem of the model on small target datasets. Finally, the GAF diagram is used as the input to the model and a feature recalibration strategy is used to adaptively obtain the importance of each feature channel, which further improves the feature utilisation. To verify the effectiveness and superiority of the proposed method, the rolling bearing data from Case Western Reserve University are selected for experimental verification and the generalisation performance of the proposed method is tested under varying loads and different dataset scales. The results show that when there is only a small amount of data, the proposed method can still achieve high diagnosis accuracy for different loads and has better recognition accuracy and generalisation compared to other fault diagnosis methods.

An island detection approach in 6G paradigm for an active distribution network – A future perspective for next generation smart grids

Aiming ultra-reliable and mountable connectivity of tremendously high data rates in the Tb/s era with zero-perceived latency of 6G systems, next generation smart grids will need to captivate the advantages of breakthrough novel technology perceptions, incorporating THz wireless links, broadband and machine learning-based models designs, protocols and management practices. Motivated by the transformation potential of 6G systems, this paper deals with an island detection approach in 6G paradigm for an active distribution network. The proposed island detection method is tailored to adopt the breakthrough technologies of 6G, particularly, ultra-low latency, high volume data transmission and machine learned intelligent system. This methodology calculates the angular sum of the positive and the zero-sequence phase angle of the voltage at point of common coupling combined with random forest (RF) machine learning to identify islanding conditions. The technique has a robust resistance to noise due to the inherent nature of RF, has no consequences on power quality and exhibits a zero non-detection zone. It has the ability to differentiate between islanding and non-islanding events precisely even during active and reactive power discrepancy and transients similar to islanding. The method depicts a high testing accuracy of 98.46% with an island detection time of 52 ms.

Investigation of rolling bearing weak fault diagnosis based on cnn with two-dimensional image

In this paper, we choose convolution neural network (CNN) as the method to diagnosis weak fault of rolling bearings. In order to improve the training effect of CNN, different two-dimensional image conversion algorithms which include Gramian angular sum difference fields, wavelet time-frequency diagram, Markov transition field are introduced in to convert one-dimensional time series of bearing vibration signals into images. To relieve the pressure of hardware calculation and shorten the time of training and validation, we use the piecewise aggregate approximation (PAA) to compress the data as much as possible while preserving the whole signal information. We add the batch normalization layer to avoid the gradient saturation problem of ReLU function and minibatch method is used to overcome the instability of stochastic gradient descent with momentum (SGDM) while designing CNN. Each kind of images are made as the training sample, and the results show that both the wavelet time-frequency diagram and the Gramian sum or difference angle field diagram can better identify the fault state, and the wavelet time-frequency diagram was relatively better. By comparing with different recurrent neural network (RNN) diagnosis models, the validity of the model was proved. At the same time, the model is applied to the performance degradation identification of fault parts, and the results shows that the model can effectively identify the degradation of inner ring, outer ring and rolling body, while the accuracy of inner ring and the outer ring is better. This paper provides a new idea for weak fault diagnosis of rolling bearings.

Leveraging a micro synchrophasor for fault detection in a renewable based smart grid—A machine learned sustainable solution with cyber-attack resiliency

The advent of renewable distributed generation has led to the rethinking of the conventional protection systems, especially during fault. A sustainable fault detection algorithm is needed to enhance the distribution system's resiliency and safety. Keeping this point of view, the paper presents a micro synchrophasor or µPMU-based fault detection algorithm with fewer probabilities of cyber-attack. In the µPMU, after obtaining the current signals, the three-phase sequence components are evaluated and the angular sum of the positive and zero sequences is recorded. The maximum angular sum is fed to a trained machine learning (random forest) classifier for fault detection. The algorithm has a high resistance to cyber-attacks and is strongly immune to noise. The method has 98.91% accuracy, 99.89% precision and exhibits a detection time of 8.5 ms. The method is cost effective as it leverages a µPMU for fault detection algorithm, reducing the need of additional hardware and software. The method also proves to be superior than other fault detection methods in terms of accuracy, precision, detection time and the capability to handle noise and cyber-attacks. All the simulations are done in MATLAB/SIMULINK for a renewable based IEEE 13 node distribution test feeder.

Strain-induced Reactivity Effects in the Reaction of 2,5-Dihydroxy-[1,4]- benzoquinone with Diamines

The regioselectivity of the reaction of 2,5-dihydroxy-[1,4]-benzoquinone (DHBQ) with diamines could not be explained satisfactorily so far. In general, the reaction products can be derived from the tautomeric ortho-quinoid structure of a hypothetical 4,5-dihydroxy- [1,2]-benzoquinone. However, both aromatic and aliphatic 1,2-diamines form phenazines, in some cases, formally by diimine formation on the quinoid carbonyl groups, and in other cases, the corresponding 1,2-diamino-[1,2]-benzoquinones by nucleophilic substitution of the OH groups; the regioselectivity apparently does not follow any discernible pattern. The reactivity was now explained by an adapted theory of strain-induced bond localization (SIBL). Here, the preservation of the "natural" geometry of the two quinoid C–C double bonds (C3=C4 and C5=C6) as well as the N–N distance of the co-reacting diamine are crucial. A decrease of the annulation angle sum (N–C4–C5 + C4–C5–N) is tolerated well and the 4,5-diamino-ortho-quinones, having relatively short N–N spacings, are formed. An increase in the angular sum is energetically unfavorable, so that diamines with a larger N–N distance afford the corresponding ortho-quinone imines. Thus, for the reaction of DHBQ with diamines, exact predictions of the regioselectivity and the resulting product structure can be made on the basis of simple computations of bond spacings and product geometries.

On the evolutionary significance of the size and planarity of the proline ring

Proline is a proteinogenic amino acid in which the side chain forms a ring, the pyrrolidine ring. This is a five-membered ring made up of four carbons and one nitrogen. Here, we study the evolutionary significance of this ring size. It is shown that the size of the pyrrolidine ring has the advantage of being nearly planar and strain-free, based on a general mathematical assertion saying that the angular sum of a polygon is maximum if it is planar and convex. We also provide a sketch of the proof to this assertion. The optimality of the ring size of proline can be derived from a triangle inequality for angles. Quasi-planarity is physiologically significant because it allows an easier and evolutionarily old type of fit into binding grooves of proteins with which proline-rich proteins interact. Finally, we present a comparison with other planar, nearly planar and non-planar biomolecules such as neurotransmitters, hormones and toxins, involving, for example, aromatic rings, cyclopentanone and 1,3-dioxole.

N,N-Dibenzoylferrocenecarboxamide

In the title compound, [Fe(C5H5)(C20H14NO3)], the cyclo­penta­dienyl rings deviate by 9.3 (2)° from an eclipsed conformation, defined by C—Cg 1—Cg 2—C pseudo-torsion angles ranging from 8.8 (1) to 9.85 (1)°. The coordination at the N atom is slightly pyramidal, as indicated by the angular sum around it of 352.6°. The amide group is inclined at 17.86 (9) and 27.27 (11)° with respect to the aromatic rings. In the crystal, mol­ecules are linked by one C—H⋯O hydrogen bond and one C—H⋯π inter­action into a two-dimensional framework parallel to the b axis.

The Riemann hypothesis and the zero distribution of angular lattice sums

We give analytical results pertaining to the distributions of zeros of a class of sums which involve complex powers of the distance to points in a two-dimensional square lattice and trigonometric functions of their angle. Let denote the product of the Riemann zeta function and the Catalan beta function, and let denote a particular set of angular sums. We then introduce a function that is the quotient of the angular lattice sums with , and use its properties to prove that obeys the Riemann hypothesis for any m if and only if obeys the Riemann hypothesis. We furthermore prove that if the Riemann hypothesis holds, then and have the same distribution of zeros on the critical line (in a sense made precise in the proof). We also show that if obeys the Riemann hypothesis and all its zeros on the critical line have multiplicity one, then all the zeros of every have multiplicity one. We give numerical results illustrating these and other results.

Validité de la somme angulaire comme technique d’extraction d’images planaires à partir de données tomoscintigraphiques pulmonaires de ventilation-perfusion

The aim of our study was to assess the concordance between the results of angular summed images obtained from lung SPECT data versus true planar images in the diagnosis of pulmonary embolism. One hundred and ten patients suspected of pulmonary embolism included in a prospective study underwent a planar lung scan and a lung SPECT. Planar images were extracted from SPECT data using an angular summing technique. Both modalities were reviewed according to revised Pioped criteria by two nuclear medicine physicians. Concordance between modalities and observers was compared with a weighted kappa test. A good degree of agreement between the two modalities (κ = 0.696) were found. Interobserver degree of agreement was similar in planar images (κ = 0.919) and in angular summed images (κ = 0.903). These results suggest that angular sum images from SPECT data are usable and concordant with ventilation perfusion planar images.

TriorganoazidometalatesCompounds with Unusual Structural Motifs

The reaction of Ga(CH2Ph)3 with CsN3 in THF gives, after recrystallization from toluene, the metalate [Cs(toluene)0.5{(PhCH2)3GaN3}] (1), whereas the corresponding reaction of In(CH2Ph)3 with CsN3 in THF yields, after recrystallization from toluene, the solvent-free salt Cs[(PhCH2)3InN3] (2). 1 and 2 have been characterized by NMR, IR, and MS techniques as well as by X-ray analyses. According to the X-ray structure determination, 1 and 2 can be described as coordination polymers [1]n and [2]n in the solid state. [1]n consists of layers, packed along the crystallographic a-axis. The monomers 1 are connected by Cs···N3 and Cs···aryl contacts to form polymeric sheets. [2]n mainly consists of chains aligned along the directions [011] and [011̄]. Here, the monomers 2 are connected by Cs···phenyl contacts. In addition, weak In···N3 interactions of 2.901(5) Å are observed, leading to a strongly distorted trigonal bipyramidal coordination sphere of the indium center (angular sum, equatorial plane, 355°) and to a cross-linking of the chains in the direction [100].

Contribution of Frank ECG measurements to the quantitative estimation of old anterior myocardial infarction

Twenty scalar and vector measurements of the Frank ECG were compared between men categorized as having suffered nontransmural ( n = 47) and transmural anterior myocardial infarction ( n = 124), on the basis of clinical and angiocardiographic findings. Variables which showed significant differences of group means between cases with anterior wall hypokinesis and anterior wall akinesis and/or dyskinesis were submitted to linear discriminant-function analysis. The stepwise selection procedure of Rao's method demonstrated the three most decisive variables for differentiation to be: (1) the angular sum of dorsal displacement of the 5 initial QRS vectors obtained at 0.01 sec intervals (sum of negative azimuth angles); (2) the Q duration in lead Z (anterior force); and (3) the Q duration in lead X (rightward force). The classification routine can identify correctly 81% of the nontransmural and 79% of the transmural anterior infarctions. The high percentages of correctly classified nontransmural and transmural infarctions show significant diagnostic potential for patient management. From the results of discriminant-function analysis, it is apparent that the sum of negative azimuth angles derived from the dorsally directed vectors during the first half of QRS exceeds substantially the scalar variables in their contribution to differentiation of the two conditions.

A finite difference method of solving anisotropic scattering problems

A new method of solving radiative transfer problems is described including a comparison of its speed with that of the doubling method, and a discussion of its accuracy and suitability for computations involving variable optical properties. The method uses a discretization in angle to produce a coupled set of first-order differential equations which are integrated between discrete depth points to produce a set of recursion relations for symmetric and anti-symmetric angular sums of the radiation field at alternate depth points. The formulation given here includes depth-dependent anisotropic scattering, absorption, and internal sources, and allows arbitrary combinations of specular and non-Lambertian diffuse reflection at either or both boundaries. The method is shown to be faster than the doubling method when the number of depth points and angular quadrature points is identical. Numerical tests of the method show that it can return accurate emergent intensities even for large optical depths. The method is also shown to conserve flux to machine accuracy in conservative atmospheres. Finally, several checks are made that demonstrate that the new method can compute accurate radiation fields in atmospheres with variable optical properties.

Shape-oriented storage and retrieval of geometric figures and chromosome images

Four advantages of storing and retrieving geometric figures and chromosome images through the use of shape-oriented similarity measures are presented. A complemented but not distributive lattice and a distributive but not complemented lattice are found. Answers to triangle related fuzzy queries such as “retrieve the triangles which are very similar to isosceles triangles but not similar to a given triangle Δ x”, and chromosome related fuzzy queries such as “retrieve the chromosomes which are more or less similar to median chromosomes and very very similar to a given chromosome A” are presented and illustrated by examples. For shape-oriented storage of triangles, it is proposed to store the angles of each triangle in decreasing order of the magnitude and logically order all the triangles according to the magnitude of the angles. For shape-oriented storage of chromosomes, it is proposed to logically order all the chromosomes individually and independently according to the angular sums of its exterior biangles and interior biangles. The results may have useful applications in information storage and retrieval, artificial intelligence and pattern recognition.

Orthogonal properties of a set of 2-path filters

The known form of 2-path filter is shown to be one of a set of four structures which correspond to the sine and cosine of angular sum and difference formulas of elementary trigonometry. Two of these structures are shown to be components of the general orthogonal 2-port network and therefore useful for synthesis purposes.