A review on prognostic techniques for non-stationary and non-linear rotating systems

The field of prognostics has attracted significant interest from the research community in recent times. Prognostics enables the prediction of failures in machines resulting in benefits to plant operators such as shorter downtimes, higher operation reliability, reduced operations and maintenance cost, and more effective maintenance and logistics planning. Prognostic systems have been successfully deployed for the monitoring of relatively simple rotating machines. However, machines and associated systems today are increasingly complex. As such, there is an urgent need to develop prognostic techniques for such complex systems operating in the real world. This review paper focuses on prognostic techniques that can be applied to rotating machinery operating under non-linear and non-stationary conditions. The general concept of these techniques, the pros and cons of applying these methods, as well as their applications in the research field are discussed. Finally, the opportunities and challenges in implementing prognostic systems and developing effective techniques for monitoring machines operating under non-stationary and non-linear conditions are also discussed.

Group 14 element-based non-centrosymmetric quantum spin hall insulators with large bulk gap

To date, a number of two-dimensional (2D) topological insulators (TIs) have been realized in Group 14 elemental honeycomb lattices, but all are inversionsymmetric. Here, based on first-principles calculations, we predict a new family of 2D inversion-asymmetric TIs with sizeable bulk gaps from 105 meV to 284 meV, in X2–GeSn (X = H, F, Cl, Br, I) monolayers, making them in principle suitable for room-temperature applications. The nontrivial topological characteristics of inverted band orders are identified in pristine X2–GeSn with X = (F, Cl, Br, I), whereas H2–GeSn undergoes a nontrivial band inversion at 8% lattice expansion. Topologically protected edge states are identified in X2–GeSn with X = (F, Cl, Br, I), as well as in strained H2–GeSn. More importantly, the edges of these systems, which exhibit single-Dirac-cone characteristics located exactly in the middle of their bulk band gaps, are ideal for dissipationless transport. Thus, Group 14 elemental honeycomb lattices provide a fascinating playground for the manipulation of quantum states.

Inferential, non-parametric statistics to assess quality of probabilistic forecast systems

Many statistical forecast systems are available to interested users. In order to be useful for decision-making, these systems must be based on evidence of underlying mechanisms. Once causal connections between the mechanism and their statistical manifestation have been firmly established, the forecasts must also provide some quantitative evidence of `quality’. However, the quality of statistical climate forecast systems (forecast quality) is an ill-defined and frequently misunderstood property. Often, providers and users of such forecast systems are unclear about what ‘quality’ entails and how to measure it, leading to confusion and misinformation. Here we present a generic framework to quantify aspects of forecast quality using an inferential approach to calculate nominal significance levels (p-values) that can be obtained either by directly applying non-parametric statistical tests such as Kruskal-Wallis (KW) or Kolmogorov-Smirnov (KS) or by using Monte-Carlo methods (in the case of forecast skill scores). Once converted to p-values, these forecast quality measures provide a means to objectively evaluate and compare temporal and spatial patterns of forecast quality across datasets and forecast systems. Our analysis demonstrates the importance of providing p-values rather than adopting some arbitrarily chosen significance levels such as p < 0.05 or p < 0.01, which is still common practice. This is illustrated by applying non-parametric tests (such as KW and KS) and skill scoring methods (LEPS and RPSS) to the 5-phase Southern Oscillation Index classification system using historical rainfall data from Australia, The Republic of South Africa and India. The selection of quality measures is solely based on their common use and does not constitute endorsement. We found that non-parametric statistical tests can be adequate proxies for skill measures such as LEPS or RPSS. The framework can be implemented anywhere, regardless of dataset, forecast system or quality measure. Eventually such inferential evidence should be complimented by descriptive statistical methods in order to fully assist in operational risk management.

Dynamic Bayesian network inferencing for non-homogeneous complex systems

Dynamic Bayesian Networks (DBNs) provide a versatile platform for predicting and analysing the behaviour of complex systems. As such, they are well suited to the prediction of complex ecosystem population trajectories under anthropogenic disturbances such as the dredging of marine seagrass ecosystems. However, DBNs assume a homogeneous Markov chain whereas a key characteristics of complex ecosystems is the presence of feedback loops, path dependencies and regime changes whereby the behaviour of the system can vary based on past states. This paper develops a method based on the small world structure of complex systems networks to modularise a non-homogeneous DBN and enable the computation of posterior marginal probabilities given evidence in forwards inference. It also provides an approach for an approximate solution for backwards inference as convergence is not guaranteed for a path dependent system. When applied to the seagrass dredging problem, the incorporation of path dependency can implement conditional absorption and allows release from the zero state in line with environmental and ecological observations. As dredging has a marked global impact on seagrass and other marine ecosystems of high environmental and economic value, using such a complex systems model to develop practical ways to meet the needs of conservation and industry through enhancing resistance and/or recovery is of paramount importance.

Improving management of summer weeds in dryland cropping systems with Cotton

In 2001 a scoping study (phase I) was commissioned to determine and prioritise the weed issues of cropping systems with dryland cotton. The main findings were that the weed flora was diverse, cropping systems complex, and weeds had a major financial and economical impact. Phase II 'Best weed management strategies for dryland cropping systems with cotton' focused on improved management of the key weeds, bladder ketmia, sowthistle, fleabane, barnyard grass and liverseed grass.In Phase III 'Improving management of summer weeds in dryland cropping systems with cotton', more information on the seed-bank dynamics of key weeds was gained in six pot and field studies. The studies found that these characteristics differed between species, and even climate in the case of bladder ketmia. Species such as sowthistle, fleabane and barnyard grass emerged predominately from the surface soil. Sweet summer grass was also in this category but also had a significant proportion emerging from 5 cm depth. Bladder ketmia in central Queensland emerged mainly from the top 2 cm, whereas in southern Queensland it emerged mainly from 5 cm. Liverseed grass had its highest emergence from 5 cm below the surface. In all cases the persistence of seed increased with increasing soil depth. Fleabane was also found to be sensitive to soil type with no seedlings emerging in the self-mulching black vertisol soil. A strategic tillage trial showed that burial of fleabane seed, using a disc or chisel plough, to a depth of greater than 2 cm can significantly reduce subsequent fleabane emergence. In contrast, tillage increased barnyard grass emergence and tended to decrease persistence. This research showed that weed management plans can not be blanketed across all weed species, rather they need to be targeted for each main weed species.This project has also resulted in an increased knowledge of how to manage fleabane from the eight experiments; one in wheat, two in sorghum, one in cotton and three in fallow on double knock. For summer crops, the best option is to apply a highly effective fallow treatment prior to sowing the crops. For winter crops, the strategy is the integration of competitive crops, residual herbicide followed by a knockdown to control survivors. This project explored further the usefulness of the double knock tactic for weed control and preventing seed set. Two field and one pot experiments have shown that this tactic was highly effective for fleabane control. Paraquat products provided good control when followed by glyphosate. When 2, 4-D was added in a tank mix with glyphosate and followed by paraquat products, 99-100% control was achieved in all cases. The ideal follow-up times for paraquat products after glyphosate were 5-7 days. The preferred follow-up times for 2, 4-D after glyphosate were on the same day and one day later. The pot trial, which compared a population from a cropping field with previous glyphosate exposure and a population from a non-cropping area with no previous glyphosate herbicide exposure, showed that the pervious herbicide exposure affected the response of fleabane to herbicidal control measures. The web-based brochure on managing fleabane has been updated.Knowledge on management of summer grasses and safe use of residual herbicides was derived from eight field and pot experiments. Residual grass and broadleaf weed control was excellent with atrazine pre-plant and at-planting treatments, provided rain was received within a short interval after application. Highly effective fallow treatments (cultivation and double knock), not only gave excellent grass control in the fallow, also gave very good control in the following cotton. In the five re-cropping experiments, there were no adverse impacts on cotton from atrazine, metolachlor, metsulfuron and chlorsulfuron residues following use in previous sorghum, wheat and fallows. However, imazapic residues did reduce cotton growth.The development of strategies to reduce the heavy reliance on glyphosate in our cropping systems, and therefore minimise the risk of glyphosate resistance development, was a key factor in the research undertaken. This work included identifying suitable tactics for summer grass control, such as double knock with glyphosate followed by paraquat and tillage. Research on fleabane also concentrated on minimising emergence through tillage, and applying the double knock tactic. Our studies have shown that these strategies can be used to prevent seed set with the goal of driving down the seed bank. Utilisation of the strategies will also reduce the reliance on glyphosate, and therefore reduce the risk of glyphosate resistance developing in our cropping systems.Information from this research, including ecological and management data were collected from an additional eight paddock monitoring sites, was also incorporated into the Weeds CRC seed bank model "Weed Seed Wizard", which will be able to predict the impact of different management options on weed populations in cotton and grain farming systems. Extensive communication activities were undertaken throughout this project to ensure adoption of the new strategies for improved weed management and reduced risk for glyphosate resistance.

Construction of stability multipliers for non-linear feedback systems

This paper is concerned with the analysis of the absolute stability of a non-linear autonomous system which consists of a single non-linearity belonging to a particular class, in an otherwise linear feedback loop. It is motivated from the earlier Popovlike frequency-domain criteria using the ' multiplier ' eoncept and involves the construction of ' stability multipliers' with prescribed phase characteristics. A few computer-based methods by which this problem can be solved are indicated and it is shown that this constitutes a stop-by-step procedure for testing the stability properties of a given system.

The pulse response of non-linear third order systems

The response of a third order non-linear system subjected to a pulse excitation is analysed. A transformation of the displacement variable is effected. The transformation function chosen is the solution of the linear problem subjected to the same pulse. With this transformation the equation of motion is brought into a form in which the method of variation of parameters is applicable for the solution of the problem. The method is applied to a single axis gyrostabilized platform subjected to an exponentially decaying pulse. The analytical results are compared with digital and analog computer solutions.

Stability of systems with power-law non-linearities

It is shown that a sufficient condition for the asymptotic stability-in-the-large of an autonomous system containing a linear part with transfer function G(jω) and a non-linearity belonging to a class of power-law non-linearities with slope restriction [0, K] in cascade in a negative feedback loop is ReZ(jω)[G(jω) + 1 K] ≥ 0 for all ω where the multiplier is given by, Z(jω) = 1 + αjω + Y(jω) - Y(-jω) with a real, y(t) = 0 for t < 0 and ∫ 0 ∞ |y(t)|dt < 1 2c2, c2 being a constant associated with the class of non-linearity. Any allowable multiplier can be converted to the above form and this form leads to lesser restrictions on the parameters in many cases. Criteria for the case of odd monotonic non-linearities and of linear gains are obtained as limiting cases of the criterion developed. A striking feature of the present result is that in the linear case it reduces to the necessary and sufficient conditions corresponding to the Nyquist criterion. An inequality of the type |R(T) - R(- T)| ≤ 2c2R(0) where R(T) is the input-output cross-correlation function of the non-linearity, is used in deriving the results.

Step function response of non-linear spring mass systems in the presence of Coulomb damping

The transient response of non-linear spring mass systems with Coulomb damping, when subjected to a step function is investigated. For a restricted class of non-linear spring characteristics, exact expressions are developed for (i) the first peak of the response curves, and (ii) the time taken to reach it. A simple, yet accurate linearization procedure is developed for obtaining the approximate time required to reach the first peak, when the spring characteristic is a general function of the displacement. The results are presented graphically in non-dimensional form.

Free vibrations of non-linear cubic spring mass systems in the presence of coulomb damping

An exact solution for the free vibration problem of non-linear cubic spring mass system with Coulomb damping is obtained during each half cycle, in terms of elliptic functions. An expression for the half cycle duration as a function of the mean amplitude during the half cycle is derived in terms of complete elliptic integrals of the first kind. An approximate solution based on a direct linearization method is developed alongside this method, and excellent agreement is obtained between the results gained by this method and the exact results. © 1970 Academic Press Inc. (London) Limited.

Application of ultraspherical polynomials to non-linear autonomous systems

This paper deals with the approximate solutions of non-linear autonomous systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on the ultraspherical polynomial expansions. The method is illustrated with examples and the results are compared with the digital and analog computer solutions. There is a close agreement between the analytical and exact results.

Equivalence conditions for classes of linear and non-linear distributed parameter systems

Equivalence of certain classes of second-order non-linear distributed parameter systems and corresponding linear third-order systems is established through a differential transformation technique. As linear systems are amenable to analysis through existing techniques, this study is expected to offer a method of tackling certain classes of non-linear problems which may otherwise prove to be formidable in nature.

A Training-Based Iterative Detection/Channel Estimation Scheme for Large Non-Orthogonal STBC MIMO Systems

In this paper, we propose a training-based channel estimation scheme for large non-orthogonal space-time block coded (STBC) MIMO systems.The proposed scheme employs a block transmission strategy where an N-t x N-t pilot matrix is sent (for training purposes) followed by several N-t x N-t square data STBC matrices, where Nt is the number of transmit antennas. At the receiver, we iterate between channel estimation (using an MMSE estimator) and detection (using a low-complexity likelihood ascent search (LAS) detector) till convergence or for a fixed number of iterations. Our simulation results show that excellent bit error rate and nearness-to-capacity performance are achieved by the proposed scheme at low complexities. The fact that we could show such good results for large STBCs (e.g., 16 x 16 STBC from cyclic division algebras) operating at spectral efficiencies in excess of 20 bps/Hz (even after accounting for the overheads meant for pilot-based channel estimation and turbo coding) establishes the effectiveness of the proposed scheme.