Balanced Reduction Research Articles

A geometric approach to nonlinear dissipative balanced reduction II: internal isometries

This Part II provides structural aspects of the internal signals and operators used in the unified geometric theory for nonlinear dissipative and Hankel balanced reduction using the differential-geometric framework based on dissipativity theory, Lie-semigroups and submanifold Hilbert theory. In particular, a novel characterization of the nonlinear Gramians is presented along with an alternative view of some concepts of the theory of nonlinear balanced reduction and the Hankel operator, namely eigenvalue problems and eigenfunction decomposition, etc.

A geometric approach to nonlinear dissipative balanced reduction I: exogenous signals

This paper is divided into two parts and provides a unified geometric theory for nonlinear dissipative and Hankel balanced reduction with the help of a framework based on differential geometry, dissipativity theory, Lie-semigroups and sub manifold Hilbert theory. Part I presents a theory for the invariants of the behavior using classical Gauss’ curvature theory. Furthermore, known concepts of the theory of balanced reduction like the Hankel operator, Schmidt decomposition, etc., can be understood in a proper and general perspective.

Model order-reduction for discrete-time switched linear systems

This article describes the problem of model order-reduction for a class of hybrid discrete-time switched linear systems composed of linear discrete-time invariant subsystems with a switching rule. This article investigates two novel approaches to model order-reduction. The first approach consists in evaluating the error approximation performance; the problems are solved using the robust stability results of the switched systems. The second approach presents the reachability and observability Gramians of the switched systems, which allows a balanced truncation model reduction procedure. A numerical example shows the effectiveness of the proposed approaches.

Hydrogen trapping: Synergetic effects of inorganic additives with cobalt sulfide absorbers and reactivity of cobalt polysulfide

The biphasic product CoS2 + Co(OH)2 obtained by oxidation of cobalt sulfide is known to trap hydrogen at room temperature and low pressure according to a balanced reduction equation. Adding various inorganic compounds to this original absorber induces their reduction by hydrogen in the same conditions at a significant rate: (i) excess cobalt hydroxide is reduced to metallic cobalt; (ii) nitrate ions are reduced to ammonia; (iii) sulfur and sodium thiosulfate are reduced to H2S or NaHS and Na2S, respectively. Without a hydrogen absorber these inorganic compounds are not reduced by H2, suggesting synergetic effects involving H2 and the hydrogen absorber. Amorphous cobalt polysulfide, CoS5, is also reduced by hydrogen at room temperature and releases H2S gas. In the presence of a base to neutralize H2S gas, the reaction rate is initially slower than with the CoS2 + Co(OH)2 mixture due to the higher stability of polysulfide chains but the H2 trapping yield is improved, making CoS5 a good candidate for H2 trapping.

Cerebral circulation, neurological and neuropsychological disorders in idiopathic arterial hypotension

Objective: to evaluate the cerebral circulation in idiopathic arterial hypotension (IAH) in relation to neurological and neuropsychological disorders. Patients and methods. Sixty-five patients (mean age 40.2 [8, 14] years) with prolonged IAH were examined. Neuropsychological examination was made using the procedure adapted by A.R. Luria; different psychic functions (memory, speech, gnosis, praxis, thinking, attention, counting, writing, and reading) were studied. Cerebral hemodynamics was investigated using duplex scanning of the brachiocephalic arteries (BCA), middle cerebral arteries (MCA), internal jugular (IJV) and vertebral veins (VV). The patients were assigned to 2 groups: 1) 19 (29%) patients with somatoform disorders, 2) 46 (71%) patients with signs of the initial manifestations of chronic cerebrovascular insufficiency. Group 2 patients were older and had a longer history of IAH. Results. In all the patients, cerebral blood supply in the carotid system showed moderately lower arterial blood inflow with a compensatory vascular resistance decrease and balanced venous outflow reduction with increased vascular resistance. Group 2 patients had a substantial (to the lower normal range) blood flow decline in the vertebral artery along with increased peripheral resistance in the VV. The degree of neuropsychological derangement was inversely proportional to blood flow velocity in BCA and MCA and to blood outflow in IJV and VV.

Relative error model reduction via time-weighted balanced stochastic singular perturbation

A new mixed method for relative error model reduction of linear time-invariant systems is proposed in this paper. This order reduction technique is mainly based upon the time-weighted balanced stochastic model reduction method and singular perturbation model reduction technique. Compared to the other analogous counterparts, the proposed method provides more accurate results in terms of time-weighted norms when applied to the practical examples. It is shown that important properties of the time-weighted stochastic balanced reduction technique are extended to the mixed reduction method by using the concept and properties of the reciprocal systems. The results are further illustrated by two practical numerical examples: a model of compact disc player and a model of the atmospheric storm track.

Generalised gramian framework for model/controller order reduction of switched systems

In this article, a general method for model/controller order reduction of switched linear dynamical systems is presented. The proposed technique is based on the generalised gramian framework for model reduction. It is shown that different classical reduction methods can be developed into a generalised gramian framework. Balanced reduction within a specified frequency bound is developed within this framework. In order to avoid numerical instability and also to increase the numerical efficiency, generalised gramian‐based Petrov–Galerkin projection is constructed instead of the similarity transform approach for reduction. The framework is developed for switched controller reduction. To the best of our knowledge, there is no other reported result on switched controller reduction in the literature. The method preserves the stability under an arbitrary switching signal for both model and controller reduction. Furthermore, it is applicable to both continuous and discrete time systems for different classical gramian‐based reduction methods. The performance of the proposed method is illustrated by numerical examples.

Transient flow control for an artificial open channel based on finite difference method

The particular challenges of modeling control systems for the middle route of the south-to-north water transfer project are illustrated. Open channel dynamics are approximated by well-known Saint-Venant nonlinear partial differential equations. For better control purpose, the finite difference method is used to discretize the Saint-Venant equations to form the state space model of channel system. To avoid calculation divergence and improve control stability, balanced model reduction together with poles placement procedure is proposed to develop the control scheme. The entire process to obtain this scheme is described in this paper, important application issue is considered as well. Experimental results show the adopted techniques are properly used in the control scheme design, and the system is able to drive the discharge to the demanded set point or maintain it around a reasonable range even if comes across big withdrawals.

A301 MIMO PID制御器の設計と4発ティルト翼小型無人機の飛行制御への適用(OS3 自律知能無人ビークルの運動と制御3)

This paper presents a design method of an MIMO (Multiple-Input-Multiple-Output) I-PD (Integral preceded by Proportional-Derivative) controller, which is a kind of PID controller, via integral-type optimal servomechanism and fractional balanced reduction (FBR) of a plant model. FBR is a kind of closed-loop model reduction method. The validity of the obtained reduced plant model is evaluated using the v-gap metric. The design method is applied to flight control design of a quad-tilt-wing (QTW) unmanned aerial vehicle (UAV).

Adli Tıp Uzman ve Asistanlarında Örgütsel Stres Düzeyi ve Etkileyen Faktörler

Çalışanlar, iş ortamındaki birçok faktör nedeniyle strese maruz kalır ve bu stres nedeniyle de fiziksel, ruhsal ve sosyal değişiklikler yaşar. Bu çalışmada; adli tıp uzman ve asistanlarının örgütsel stres düzeyinin ve stres düzeyini etkileyebilecek sosyo-demografik değişkenlerin ortaya konulması amaçlanmıştır. Örgütsel stres faktörlerinin düzeyini belirlemede Örgütsel Stres Anketi-D (VOS-D) kullanılmıştır. Anketin Türkçe versiyonu 27 ilden 120 adli tıp uzman/asistanına e-mail ya da posta ile gönderilmiş, 113’ü anketi doldurarak geri göndermiştir. Elde edilen veriler paket istatistik programı kullanılarak analiz edilmiştir. Çalışmaya katılanların 78’i (%69) üniversitelerin adli tıp anabilim dallarında, 28’i (%24.8) Adli Tıp Kurumu ve buna bağlı birimlerde, 7’si de (%6.2) Sağlık Bakanlığı’na bağlı hastanelerde görev yapmaktadır. Katılımcıların 70’i (%61.9) adli tıp uzmanı, 43’ü (%38.1) adli tıp asistanıdır. Adli tıp uzman ve asistanlarının 87’si (%77) erkek, 26’sı (%23) kadındır ve yaş ortalaması 35.9 + 7.3 (25-62) yıldır. Yanıtlanan ölçeklerin persantil dağılımına ve ortalama skorlara bakıldığında; katılımcıların ilk sırada sorumluluk, ikinci sırada aşırı iş yükünden etkilendiği görülmektedir. Stres faktörlerinden etkilenme açısından cinsiyetler arasmda istatistiksel olarak anlamlı fark bulunmamaktadır. Rol belirsizliği ve gelecek belirsizliği en çok adli tıp asistanlarını etkilerken, sorumluluk adli tıp uzmanlarında daha fazla stres yaratmaktadır. Sonuç olarak; adli tıp uzman ve asistanlarının, çalışma ortamında karşılaştığı stres faktörlerinin en aza indirgenebilmesi için, sorumluluğun paylaşılması, iş yükünün dengelenerek azaltılması gibi birtakım önlemler alınması gerekmektedir.Anahtar kelimeler: Adli tıp, örgütsel stres

Closed form ℒ 2/ℋ2-optimising of zeros for model reduction of linear continuous time systems

Closed form expressions of transfer function responses are applied in this article to model reduction of nth order continuous time systems with respect to the location of zeros for a given location of poles. Explicit closed form formulae are derived for the numerator coefficients in the transfer function of the reduced system that minimise the integrated square deviation from the original system with respect to the impulse response or higher order responses, i.e. effective ℒ2 or ℋ2-optimisation. The relative degree of the reduced model can be selected freely, e.g. as the original model's one, by selecting the number of numerator coefficients. Constraints are dealt with by introducing a vector of Lagrange multipliers corresponding to the response order. The formulae are also related to solutions of Lyapunov and Sylvester equations based on the companion matrices of the original and reduced systems. The formulae derived can be used to enhance the results obtained from other reduction techniques such as those based on balanced Grammian reduction and singular value decomposition for mid-sized systems. Two examples, demonstrating this, are presented. The formulae can also be used as a basis for a more general optimisation approach, where the optimisation with respect to the numerator coefficients or the zeros, resulting in the solution of a linear system of equations, is combined with non-linear optimisation with respect to the denominator coefficients or the poles.

Frequency-domain generelaized singular peruturbation method for relative error model order reduction

A new mixed method for relative error model order reduction is proposed. In the proposed method the frequency domain balanced stochastic truncation method is improved by applying the generalized singular perturbation method to the frequency domain balanced system in the reduction procedure. The frequency domain balanced stochastic truncation method, which was proposed in [15] and [17] by the author, is based on two recently developed methods, namely frequency domain balanced truncation within a desired frequency bound and inner-outer factorization techniques. The proposed method in this paper is a carry over of the frequency-domain balanced stochastic truncation and is of interest for practical model order reduction because in this context it shows to keep the accuracy of the approximation as high as possible without sacrificing the computational efficiency and important system properties. It is shown that some important properties of the frequency domain stochastic balanced reduction technique are extended to the proposed reduction method by using the concept and properties of the reciprocal systems. Numerical results show the accuracy, simplicity and flexibility enhancement of the method.

Discrete Time-delay Optimal Control of Structures under Seismic Excitations using the Balanced Reduction Scheme

The time-delay discrete-time equations are derived directly from the differential vibration equations for structures in state space, with discrete parameters obtained via the precise integration method. Then a state vector expansion method is used to transform these equations into ones which do not contain time-delay terms explicitly. Next, the order of this system is substantially reduced by using the balanced reduction method to form a dominant subsystem which is based on the eigenmodes of the state subspace with highest controllability. The controllers are then designed by the discrete time-delay optimal control theory, which contains the control terms not only of the current state but also of a few previous states, in order to reflect the effect of time delays. By using the proposed method, the order of the controller is very substantially reduced without causing any essential difference in the control effect. A numerical example for a shear-type building is presented and it shows the effectiveness of the proposed method even when time delays are quite large.

Switched Systems Reduction Framework Based on Convex Combination of Generalized Gramians

A general method for model-order reduction of switched linear dynamical systems is presented. The proposed technique uses convex generalized gramian which is a convex combination of the generalized gramians. It is shown that different classical reduction methods can be developed into the generalized gramian framework for model reduction of linear systems and further for the reduction of switched systems by construction of the convex generalized gramian. Balanced reduction within specified frequency bound is taken as an example which is developed within this framework. In order to avoid numerical instability and also to increase the numerical efficiency, convex generalized gramian-based Petrov-Galerkin projection is constructed instead of the similarity transform approach for reduction. It is proven that the method preserves the stability of the original switched system at least for stabilizing switching signal and it is also less conservative than the method which is based on the common generalized gramian. Some discussions on the coefficient of the vertices of the convex variables are presented. The performance of the proposed method is illustrated by numerical examples.

H.INF. Controller Reduction by D-R Iteration Method Based on the Free-Parameter

In this paper, a new H∞ controller reduction method which considers to maintain the H∞ property is proposed. The generalized H∞-controllers are able to described using free-parameters which are stabe and bounded. If a low order controller can be written with a free-parameter which satisfies the stability and the bounded condition, the low order controller become an H∞-controller. In order to satisfy the conditions, we employ an iteration method which contains the D-scaling matrix calculation and the balanced model reduction. Some numerical examples are illustrated to show the effectiveness of our method.

Model-based traffic control for balanced reduction of fuel consumption, emissions, and travel time

In this paper we integrate the macroscopic traffic flow model METANET with the microscopic dynamic emission and fuel consumption model VT-Micro. We use the integrated models in the model predictive control (MPC) framework to reduce exhaust emissions, fuel consumption, and travel time using dynamic speed limit control. With simulation experiments we demonstrate the countereffects and conflicting nature of the different traffic control objectives. Our simulation results indicate that a model-based traffic control approach, particularly MPC, can be used to obtain a balanced trade-off between the conflicting traffic control objectives.

Balanced truncation model reduction of second-order systems

In this paper we consider structure-preserving model reduction of second-order systems using a balanced truncation approach. Several sets of singular values are introduced for such systems, which lead to different concepts of balancing and different second-order balanced truncation methods. A comparison of these methods with other second-order balanced truncation techniques is presented. We also show that, in general, none of the existing structure-preserving balanced truncation methods for second-order systems preserves stability in the reduced models. Numerical examples are given that demonstrate the properties of the new methods.

Abstract 1571: Hibernating Myocardium has Reduced High Energy Phosphate Levels and a Preconditioning-Like Effect with Slower ATP Depletion in Response to Acute Ischemia

Background. Pigs with a chronic LAD stenosis develop hibernating myocardium with contractile dysfunction and reduced resting flow. We hypothesized that this reduced energy utilization preserves ATP and protects the heart from irreversible injury during acute ischemia. Methods. Pigs with hibernating myocardium were studied 3-months after instrumentation with a 1.5 mm proximal LAD stenosis (n=7). Hibernating myocardium was confirmed by reduced LAD wall thickening (2.4±0.2 vs.6.1±0.6 mm in remote, p<0.05) and reduced resting flow (0.95±0.15 vs. 1.66±0.29 ml/min/g in remote, p<0.05) without infarction. Subendocardial samples were rapidly excised from propofol anesthetized pigs and serial depletion of high energy phosphates quantified by HPLC (in μmol/g dry weight) during simulated total ischemia in vitro (37°C). Results. At Baseline, ATP and ADP were significantly reduced in the hibernating LAD region in comparison to controls (n=8, Table ), with preserved CP/ATP and ATP/ADP ratios. During simulated ischemia, hibernating myocardium displayed a markedly reduced rate of ATP depletion (ΔATP), with ATP levels at 20 min significantly higher than control (Table ). Higher ATP levels were maintained throughout 80 min of ischemia. Interestingly, identical preservation of high energy phosphates occurred in the remote normally perfused region of hearts with hibernating myocardium (Table ). Conclusion. These data indicate that there is a balanced reduction in high energy phosphate levels in hibernating myocardium with chronic protection from ischemia manifested by a slower rate of ATP depletion during acute ischemia. This preconditioning-like effect is global suggesting that it arises from stimuli that are not directly related to ischemia. This raises the possibility that stretch from cyclical elevations in LV filling pressure or a circulating factor released from the heart in response to ischemia can protect the heart in chronic coronary artery disease.

Adapting regional eutrophication targets for surface waters—influence of the EU Water Framework Directive, national policy and climate change

Large amounts of waterborne nutrients are major problems for society since they can cause harmful algal blooms in surface water bodies. Consequently, there are a variety of national and international guidelines, e.g. Swedish National Environmental Quality Objectives and the EU Water Framework Directive, which include targets to be achieved within a certain time frame. This paper uses the example of a large Swedish lake to show that national and international targets must be adapted to the local situations. Despite decreasing nutrient concentrations, cyanobacterial blooms in the lake have increased over recent years. We found that these blooms coincide with depleted nitrate–nitrogen concentrations and increased water temperatures. We propose a simple model with water temperature, nitrate–nitrogen and total phosphorus concentrations as input variables as a basis for formulation of regional eutrophication targets. Political decisions should be preceded by open discussion between policymakers and scientists to differentiate between real knowledge, assumptions or feelings. For optimal results, recommendations for reducing nutrient load should consider all sources, including urban stormwater and wastewater from rural houses, and should be founded on a balanced reduction in emissions of algae-available nutrients. In addition, climate change calls for more effective environmental policy to protect surface water resources.

Reduced-order models for a smart plate

A Single Input Single Output (SISO) state space model has been developed in MATLAB using a smart plate model realised in ANSYS?. The frequency response due to a unit force, for the full model as well as the reduced unsorted and sorted models was studied. DC gain is used as the criterion for sorting. Simple reductions as well as 'modred' option of MATLAB were used for model reduction. In this paper a method of reducing modes, 'balanced reduction' will also be introduced. The method will be compared with dc and peak gain ranking methods using a smart plate model. The step and impulse responses for all the models were also studied. The model with minimum number of modes retained, and with minimum deviation from full model characteristics was identified analytically. It is proposed to use this model subsequently for vibration control applications.