Density-based Structure Research Articles

Density-Based Structure Preserving Projections Process Monitoring Model for Fused Magnesia Smelting Process

In this work, we address the monitoring problem in fused magnesia smelting process (FMSP). Our main goal is to accurately detect anomalies occurring in FMSP and isolate as few abnormal responsibility variables as possible. To this end, we propose anomaly detection method with density-based structure preserving projections (DSPP) and abnormal variable isolation method. DSPP first measures the degree of dispersion in the data set by calculating the sample distance entropy, and obtains the weight coefficients under the density constraint of the samples in the neighborhood and the non-neighbors, thereby establishing the objective function of the global-local structure preserving to obtain projections. On this basis, negative compensation statistics (NCS) is constructed to calculate contribution of abnormal variables by setting a unified standard index. Finally, the DSPP-based anomaly detection method and the abnormal variable isolation method are applied to a benchmark dataset and the practical FMSP. The experimental results confirm the effectiveness of the proposed method.

Analyzing Quality Measurements for Dimensionality Reduction

Dimensionality reduction methods can be used to project high-dimensional data into low-dimensional space. If the output space is restricted to two dimensions, the result is a scatter plot whose goal is to present insightful visualizations of distance- and density-based structures. The topological invariance of dimension indicates that the two-dimensional similarities in the scatter plot cannot coercively represent high-dimensional distances. In praxis, projections of several datasets with distance- and density-based structures show a misleading interpretation of the underlying structures. The examples outline that the evaluation of projections remains essential. Here, 19 unsupervised quality measurements (QM) are grouped into semantic classes with the aid of graph theory. We use three representative benchmark datasets to show that QMs fail to evaluate the projections of straightforward structures when common methods such as Principal Component Analysis (PCA), Uniform Manifold Approximation projection, or t-distributed stochastic neighbor embedding (t-SNE) are applied. This work shows that unsupervised QMs are biased towards assumed underlying structures. Based on insights gained from graph theory, we propose a new quality measurement called the Gabriel Classification Error (GCE). This work demonstrates that GCE can make an unbiased evaluation of projections. The GCE is accessible within the R package DR quality available on CRAN.

Study of tree-shaped optimized fins in a heat sink filled by solid-solid nanocomposite phase change material

The aim of this work is to comprehensively study the effect of the material of the simple plate and tree-shaped optimized fins on the thermal behavior of an enclosed medium filled with a nanocomposite of neopentyl glycol/CuO solid-solid PCM. Increasing the heat transfer rate using a fixed amount of material is an important task that improves the fin performance. The tree-shaped fin is optimized based upon the density-based structure optimization method. A transient model based upon the enthalpy method is employed to numerically study the thermal behavior of the enclosed medium containing the SS-PCM. The thermal performance of the heat sink with the tree-shaped optimized and simple plate fins made of different materials are explored. Results show that the aluminum and copper fins have the highest melting rate compared to the examined materials. Their melting rate is 50% higher than steel 302 in the case of flat plates, and 25% in the case of a tree structure. Also, the tree-shaped optimized fins outperform the plate structure fins by reaching the lowest temperature of the concentrated heat source and temperature non-uniformity under the condition that the two strucutures have the same height. When the two heights are different, the temperature distribution was optimized for materials with the lowest thermal conductivity. For steel materials, a 10% decrease in the maximum temperature was observed in the tree structure compared to the flat plates. Finally, it was shown that the nanoparticle fraction played a negligible role in heat transfer, as less than 1% change in melting rate and temperature parameters was obtained.

Swarm intelligence for self-organized clustering

Algorithms implementing populations of agents which interact with one another and sense their environment may exhibit emergent behavior such as self-organization and swarm intelligence. Here a swarm system, called Databionic swarm (DBS), is introduced which is able to adapt itself to structures of high-dimensional data characterized by distance and/or density-based structures in the data space. By exploiting the interrelations of swarm intelligence, self-organization and emergence, DBS serves as an alternative approach to the optimization of a global objective function in the task of clustering. The swarm omits the usage of a global objective function and is parameter-free because it searches for the Nash equilibrium during its annealing process.To our knowledge, DBS is the first swarm combining these approaches. Its clustering can outperform common clustering methods such as K-means, PAM, single linkage, spectral clustering, model-based clustering, and Ward, if no prior knowledge about the data is available. A central problem in clustering is the correct estimation of the number of clusters. This is addressed by a DBS visualization called topographic map which allows assessing the number of clusters. It is known that all clustering algorithms construct clusters, irrespective of the data set contains clusters or not. In contrast to most other clustering algorithms, the topographic map identifies, that clustering of the data is meaningless if the data contains no (natural) clusters. The performance of DBS is demonstrated on a set of benchmark data, which are constructed to pose difficult clustering problems and in two real-world applications.

Uncovering High-dimensional Structures of Projections from Dimensionality Reduction Methods

Projections are conventional methods of dimensionality reduction for information visualization used to transform high-dimensional data into low dimensional space. If the projection method restricts the output space to two dimensions, the result is a scatter plot. The goal of this scatter plot is to visualize the relative relationships between high-dimensional data points that build up distance and density-based structures. However, the Johnson–Lindenstrauss lemma states that the two-dimensional similarities in the scatter plot cannot coercively represent high-dimensional structures. Here, a simplified emergent self-organizing map uses the projected points of such a scatter plot in combination with the dataset in order to compute the generalized U-matrix. The generalized U-matrix defines the visualization of a topographic map depicting the misrepresentations of projected points with regards to a given dimensionality reduction method and the dataset.•The topographic map provides accurate information about the high-dimensional distance and density based structures of high-dimensional data if an appropriate dimensionality reduction method is selected.•The topographic map can uncover the absence of distance-based structures.•The topographic map reveals the number of clusters in a dataset as the number of valleys.

Numerical study of thermally optimized metal structures in a Phase Change Material (PCM) enclosure

Embedding metal fins into PCMs to improve the thermal conductance of PCM enclosure is widely used in the thermal management of mobile electronics. This paper presented the application of a density-based structure optimization method to redesign the conductive metal structure for better heat diffusion from a concentrated heat source into a PCM enclosure. Two plate fin heat sink structured PCM enclosures with the metal volume fractions of 20% and 30% were the baselines, and the optimized tree shape structures with the similar metal volume fractions of 18.7% and 27.6% were generated for comparison. A transient numerical model based on the Volume of Fluid (VOF) and enthalpy-porosity methods was built to investigate the dynamic thermal behaviors of PCM enclosures. Results illustrated that the optimized tree shape designs outperformed the baseline designs by achieving lower heat source temperature and higher melt fraction in the main PCM melting stage. Increasing metal volume fraction improved the overall thermal conductance of PCM enclosures and hence suppressed the temperature non-uniformity and lowered the heat source temperature. Upwardly orientated PCM enclosure had much better heat transfer performance than that under downward orientation due to its enhanced thermal mixing resulted from the intensified convection flows.

Fiber orientation measurement from mesoscale CT scans of prepreg platelet molded composites

X-ray computed tomography (CT) analysis is used to measure the heterogeneous fiber orientation fields in a 20 cm3 composite bracket made from prepreg platelet-based molding compound (PPMC). The as-molded mesostructure of the complete geometry is captured using material density gradients in 50 µm resolution CT scans without the need to resolve individual fibers. Fiber collimation and physical density gradients within intact platelets of this material system facilitates nondestructive assessment of average local fiber orientation at the component scale. Microscopy-based validation of the local orientation measurements indicate the accuracy that can be attained utilizing the density-based structure tensor CT analysis method. Local orientation field measurements for the complete geometry can be mapped into a “digital twin” model, for purposes such as experimental performance simulation and validation of molding process orientation state predictions. Composite designers, analysts, and material suppliers can employ this methodology to more confidently utilize PPMCs and morphologically similar composite material systems.

Phenomenological Description of a Three-Center Insertion Reaction: An Information-Theoretic Study

Information-theoretic measures are employed to describe the course of a three-center chemical reaction in terms of detecting the transition state and the stationary points unfolding the bond-forming and bond-breaking regions which are not revealed in the energy profile. The information entropy profiles for the selected reactions are generated by following the intrinsic-reaction-coordinate (IRC) path calculated at the MP2 level of theory from which Shannon entropies in position and momentum spaces at the QCISD(T)/6-311++G(3df,2p) level are determined. Several complementary reactivity descriptors are also determined, such as the dipole moment, the molecular electrostatic potential (MEP) obtained through a multipole expansion (DMA), the atomic charges and electric potentials fitted to the MEP, the hardness and softness DFT descriptors, and several geometrical parameters which support the information-theoretic analysis. New density-based structures related to the bond-forming and bond-breaking regions are proposed. Our results support the concept of a continuum of transient of Zewail and Polanyi for the transition state rather than a single state, which is also in agreement with reaction-force analyses.