Two-phase Iterative Algorithm Research Articles

Discovering Premature Replacements in Predictive Maintenance Time-to-Event Data

Time-To-Event (TTE) modeling using survival analysis in industrial settings faces the challenge of premature replacements of machine components, which leads to bias and errors in survival prediction. Typically, TTE survival data contains information about components and if they had failed or not up to a certain time. For failed components, the time is noted, and a failure is referred to as an event. A component that has not failed is denoted as censored. In industrial settings, in contrast to medical settings, there can be considerable uncertainty in an event; a component can be replaced before it fails to prevent operation stops or because maintenance staff believe that the component is faulty. This shows up as “no fault found” in warranty studies, where a significant proportion of replaced components may appear fault-free when tested or inspected after replacement. In this work, we propose an expectation-maximization-like method for discovering such premature replacements in survival data. The method is a two-phase iterative algorithm employing a genetic algorithm in the maximization phase to learn better event assignments on a validation set. The learned labels through iterations are accumulated and averaged to be used to initialize the following expectation phase. The assumption is that the more often the event is selected, the more likely it is to be an actual failure and not a “no fault found”. Experiments on synthesized and simulated data show that the proposed method can correctly detect a significant percentage of premature replacement cases.

Algorithm Design and Performance Analysis of Target Localization Using Mobile Underwater Acoustic Array Networks

Space-air-ground-sea integrated network, as a promising networking paradigm for the sixth generation (6 G) communications, connects satellite networks, aerial networks, terrestrial networks, and marine networks. As a fundamental application of marine networks, efficient target localization in the ocean is significant for many marine and underwater applications, including oceanic environmental monitoring, subsea resource exploration, and navigation safety. In this paper, to bring more scalability and feasibility of underwater localization, a mobile underwater acoustic array network is utilized to locate underwater moving targets by leveraging linear frequency modulated (LFM) signals. In the mobile underwater acoustic network, one node is constantly broadcasting LFM signals. Based on the reflected signals received by other nodes, a method that jointly utilizes the propagation delay and the Doppler effect is proposed to simultaneously estimate the position and the velocity of the moving target. Specifically, a two-phase iterative algorithm with low computational complexity is designed to improve the estimation accuracy. Closed-form expressions of positioning and velocity estimation error are also presented. Performance evaluation shows that the proposed method clearly outperforms the least squares based approach. Moreover, the estimation accuracy of the proposed method can approach the Cramér-Rao low bound (CRLB) within two iterations. Decently good localization and velocity estimation error performance can be achieved even with an array network formed by a small number of nodes.

A Novel Preheating Coordination Approach in Electrified Heat Systems

Coordinated preheating can potentially enhance the flexibility of the electricity system, thereby driving significant economic savings. In this context, this paper proposes a novel game-theory based preheating coordination scheme aimed at guaranteeing the effectiveness of collective preheating performed by a large population of households. By adopting an innovative two-phase iterative algorithm, individual households autonomously schedule their heating power allocation to seek for savings in energy bills while smartly maintaining thermal comfort. Meanwhile, the total electricity generation cost decreases at each iteration and converges to an equilibrium solution asymptotically. Compared to the centralised optimization-based energy management control methods, the proposed algorithm effectively reduces the information exchange while significantly reduces computational complexity. The simulation results indicate that the proposed coordination strategy can drive 12.30% cost saving when all households participate in the preheating scheme whereas 11.35% cost increase will be incurred if coordination is absent. Overall, the proposed preheating control algorithm simultaneously benefits both individual households and the whole system by intelligently linking local behaviour with global interests.

Data-Driven Redundant Transform Based on Parseval Frames

The sparsity of images in a certain transform domain or dictionary has been exploited in many image processing applications. Both classic transforms and sparsifying transforms reconstruct images by a linear combination of a small basis of the transform. Both kinds of transform are non-redundant. However, natural images admit complicated textures and structures, which can hardly be sparsely represented by square transforms. To solve this issue, we propose a data-driven redundant transform based on Parseval frames (DRTPF) by applying the frame and its dual frame as the backward and forward transform operators, respectively. Benefitting from this pairwise use of frames, the proposed model combines a synthesis sparse system and an analysis sparse system. By enforcing the frame pair to be Parseval frames, the singular values and condition number of the learnt redundant frames, which are efficient values for measuring the quality of the learnt sparsifying transforms, are forced to achieve an optimal state. We formulate a transform pair (i.e., frame pair) learning model and a two-phase iterative algorithm, analyze the robustness of the proposed DRTPF and the convergence of the corresponding algorithm, and demonstrate the effectiveness of our proposed DRTPF by analyzing its robustness against noise and sparsification errors. Extensive experimental results on image denoising show that our proposed model achieves superior denoising performance, in terms of subjective and objective quality, compared to traditional sparse models.

Stable Sparse Model with Non-Tight Frame

Overcomplete representation is attracting interest in image restoration due to its potential to generate sparse representations of signals. However, the problem of seeking sparse representation must be unstable in the presence of noise. Restricted Isometry Property (RIP), playing a crucial role in providing stable sparse representation, has been ignored in the existing sparse models as it is hard to integrate into the conventional sparse models as a regularizer. In this paper, we propose a stable sparse model with non-tight frame (SSM-NTF) via applying the corresponding frame condition to approximate RIP. Our SSM-NTF model takes into account the advantage of the traditional sparse model, and meanwhile contains RIP and closed-form expression of sparse coefficients which ensure stable recovery. Moreover, benefitting from the pair-wise of the non-tight frame (the original frame and its dual frame), our SSM-NTF model combines a synthesis sparse system and an analysis sparse system. By enforcing the frame bounds and applying a second-order truncated series to approximate the inverse frame operator, we formulate a dictionary pair (frame pair) learning model along with a two-phase iterative algorithm. Extensive experimental results on image restoration tasks such as denoising, super resolution and inpainting show that our proposed SSM-NTF achieves superior recovery performance in terms of both subjective and objective quality.

An Efficient Entropy-Based Causal Discovery Method for Linear Structural Equation Models With IID Noise Variables

The discovery of causal relationships from the observational data is an important task. To identify the unique causal structure belonging to a Markov equivalence class, a number of algorithms, such as the linear non-Gaussian acyclic model (LiNGAM), have been proposed. However, two challenges remain to be met: 1) these algorithms fail to work on the data which follow linear structural equation model with Gaussian noise and 2) they misjudge the causal direction when the data contain additional measurement errors. In this paper, we propose an entropy-based two-phase iterative algorithm for arbitrary distribution data with additional measurement errors under some mild assumptions. In the first phase of the algorithm, based on the property that entropy can measure the amount of information behind the data with arbitrary distribution, we design a general approach for the identification of exogenous variable on both Gaussian and non-Gaussian data, and we give the corresponding theoretical derivation. In the second phase, to eliminate the effects of measurement errors, we revise the value of the exogenous variable by removing its measurement error and further use the revised value to remove its effect on the remaining variables. Experimental results on real-world causal structures are presented to demonstrate the effectiveness and stability of our method. We also apply the proposed algorithm on the mobile-base-station data with measurement errors, and the results further prove the effectiveness of our algorithm.

A Pattern Based Method for Simplifying a BPMN Process Model

BPMN (Business Process Model and Notation) is currently the preferred standard for the representation and analysis of business processes. The elaboration of these BPMN diagrams is usually carried out in an entirely manual manner. As a result of this human-driven process, it is not uncommon to find diagrams that are not in their most simplified version possible (regarding the number of elements). This work presents a fully automatic method to simplify a BPMN process model document. A two-phase iterative algorithm to achieve this simplification is described in detail. This algorithm follows a heuristic approach that makes intensive use of a Pattern Repository. This software element is concerned with the description of feasible reductions and its enactment. The critical concept lies in the discovery of small reducible patterns in the whole model and their substitution with optimised versions. This approach has been verified through a double validation testing in total 8102 cases taken from real world BPMN process models. Details for its implementation and usage by practitioners are provided in this paper along with a comparison with other existing techniques concerned with similar goals.

Modified Shuffled Based Architecture for High-Throughput Decoding of LDPC Codes

Low Density Parity-Check (LDPC) codes achieve the best performance when they are decoded with the sum-product (SP) algorithm. This is a two-phase iterative algorithm where two types of messages are interchanged and updated in each iteration. The group-shuffled or layered decoding schemes applied to the SP algorithm speed up its convergence by modifying its schedule, so they yield a reduction in the number of iterations required to achieve a given performance. However, the two-phase processing is still maintained. In this paper a modification of the group-shuffled scheme suitable for high-rate LDPC codes is proposed. The modification allows the overlapping of the two-phase computation, achieving a convergence speed up close to that of the group-shuffled scheme with higher throughput. Besides, high throughput architectures are presented for the modified algorithm. As an example, the proposed architecture has been implemented for the 2048-bit LDPC code of the IEEE 802.3an standard and it was synthesized in a 90 nm CMOS process achieving a throughput of 22.40 Gbps at 14 iterations with a clock frequency of 306 MHz and a total area of 10.5 mm2. Furthermore, the decoder performs within 0.5 dB of the floating-point 100 iterations sum-product algorithm at a PER of 10?5.

A Two-phase Iterative Algorithm for Improved Approximation by Szasz Operator Using Statistical Perspectives

This paper aims at constructing a two-phase iterative numerical algorithm for the improved approximation of a continuous function by the ‘Modified Szasz’ operator. The algorithm uses a ‘statistical perspective’ to more fully expoit the information about the unknown function f . The improvement occurs iteratively. A typical iteration uses the twin statistical concepts of ‘Mean Square Error’ (MSE) and ‘Bias’; the application of the latter concept being preceded by that of the former in the algorithm. At any iteration, the statistical concept of ‘MSE’ is used in “Phase II”, after that of the ‘Bias’ in “Phase I”. The procedure is like a sandwich. The top and bottom slices are the operations of ‘Bias-Reduction’ in “Phase I” of the algorithm, and the operation of ‘MSE-Reduction’ in “Phase II” is the stuffing in the sandwich. The improvement acheived by this algorithm is evaluated by means of a simulation study using known functions. The simulation has been confined to three iterations only, for the sake of simplicity.

Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming

We propose to compute the search direction at each interior-point iteration for a linear program via a reduced augmented system that typically has a much smaller dimension than the original augmented system. This reduced system is potentially less susceptible to the ill-conditioning effect of the elements in the (1,1) block of the augmented matrix. A preconditioner is then designed by approximating the block structure of the inverse of the transformed matrix to further improve the spectral properties of the transformed system. The resulting preconditioned system is likely to become better conditioned toward the end of the interior-point algorithm. Capitalizing on the special spectral properties of the transformed matrix, we further proposed a two-phase iterative algorithm that starts by solving the normal equations with PCG in each IPM iteration, and then switches to solve the preconditioned reduced augmented system with symmetric quasi-minimal residual (SQMR) method when it is advantageous to do so. The experimental results have demonstrated that our proposed method is competitive with direct methods in solving large-scale LP problems and a set of highly degenerate LP problems.

Mirage: A new iterative map-making code for CMB experiments

A major goal of CMB experiments is to obtain highly sensitive CMB maps in order to extract Spherical Harmonic Power Spectrum (SHPS) and cosmological parameters with unprecedented accuracy. We present a new map-making code (Mirage), based on a two-phase iterative algorithm, involving low frequency drift treatment, Butterworth high-pass filtering and conjugate gradient method. This work was strongly motivated by Archeops CMB experiment data analysis. We believe that Archeops was a good test bench for the future Planck Surveyor data analysis, and Mirage was designed in order to be used for Planck data processing with minimal work. A strong feature of Mirage is that it handles experimental problems in data, such as holes in data stream, bright sources, and galaxy side effects, without jeopardising speed. The other advantage is its processing speed, allowing to run Monte Carlo simulations of Archeops data processing on a single processor workstation overnight. Algorithms are explained. Systematic effects on SHPS are investigated on various simulated data, including typical Archeops observational systematics. This code is available at adress http://www-dapnia.cea.fr/Telechargement/ Preprint with full resolution figures is available at http://www-dapnia.cea.fr/Doc/Publications/Archives/dapnia-03-378.pdf