Stability analysis of tree structured decision functions

In multicriteria decision problems many values must be assigned, such as the importance of the different criteria and the values of the alternatives with respect to subjective criteria. Since these assignments are approximate, it is very important to analyze the sensitivity of results when small modifications of the assignments are made. When solving a multicriteria decision problem, it is desirable to choose a decision function that leads to a solution as stable as possible. We propose here a method based on genetic programming that produces better decision functions than the commonly used ones. The theoretical expectations are validated by case studies. © 2003 Elsevier B.V. All rights reserved.

Recent Results on Stability Analysis of an Optimal Assembly Line Balance

Two assembly line balancing problems are addressed. The first problem (called SALBP-1) is to minimize number of linearly ordered stations for processing n partially ordered operations V = {1, 2, ..., n} within the fixed cycle time c. The second problem (called SALBP-2) is to minimize cycle time for processing partially ordered operations V on the fixed set of m linearly ordered stations. The processing time ti of each operation i ∈V is known before solving problems SALBP-1 and SALBP-2. However, during the life cycle of the assembly line the values ti are definitely fixed only for the subset of automated operations V\V . Another subset V ⊆ V includes manual operations, for which it is impossible to fix exact processing times during the whole life cycle of the assembly line. If j ∈V , then operation times tj can differ for different cycles of the production process. For the optimal line balance b of the assembly line with operation times t1, t2, ..., tn, we investigate stability of its optimality with respect to possible variations of the processing times tj of the manual operations j ∈ V .

Multiscale Schemes for the BGK--Vlasov--Poisson System in the Quasi-Neutral and Fluid Limits. Stability Analysis and First Order Schemes

This paper deals with the development and the analysis of asymptotically stable and consistent schemes in the joint quasi-neutral and fluid limits for the collisional Vlasov-Poisson system. In these limits, the classical explicit schemes suffer from time step restrictions due to the small plasma period and Knudsen number. To solve this problem, we propose a new scheme stable for choices of time steps independent from the small scales dynamics and with comparable computational cost with respect to standard explicit schemes. In addition, this scheme reduces automatically to consistent discretizations of the underlying asymptotic systems. In this first work on this subject, we propose a first order in time scheme and we perform a relative linear stability analysis to deal with such problems. The framework we propose permits to extend this approach to high order schemes in the next future. We finally show the capability of the method in dealing with small scales through numerical experiments.

SLOPE STABILITY ANALYSIS OF MOUNT MEAGER, SOUTH-WESTERN BRITISH COLUMBIA, CANADA

The Mount Meager Volcanic Complex (MMVC) in south-western British Columbia is a potentially active, hydrothermally altered massif comprising a series of steep, glaciated peaks. Climatic conditions and glacial retreat has led to the further weathering, exposure and de-buttressing of steep slopes composed of weak, unconsolidated material. This has resulted in an increased frequency of landslide events over the past few decades, many of which have dammed the rivers bordering the Complex. The breach of these debris dams presents a risk of flooding to the downstream communities. Preliminary mapping showed there are numerous sites around the Complex where future failure could occur. Some of these areas are currently undergoing progressive slope movement and display features to support this such as anti-scarps and tension cracks. The effect of water infiltration on stability was modelled using the Rocscience program Slide 6.0. The main site of focus was Mount Meager in the south- east of the Complex where the most recent landslide took place. Two profiles through Mount Meager were analysed along with one other location in the northern section of the MMVC, where instability had been detected. The lowest Factor of Safety (FOS) for each profile was displayed and an estimate of the volume which could be generated was deduced. A hazard map showing the inundation zones for various volumes of debris flows was created from simulations using LAHARZ. Results showed the massif is unstable, even before infiltration. Varying the amount of infiltration appears to have no significant impact on the FOS annually implying that small changes of any kind could also trigger failure. Further modelling could be done to assess the impact of infiltration over shorter time scales. The Slide models show the volume of material that could be delivered to the Lillooet River Valley to be of the order of 109 m3 which, based on the LAHARZ simulations, would completely inundate the valley and communities downstream. A major hazard of this is that the removal of such a large amount of material has the potential to trigger an explosive eruption of the geothermal system and renew volcanic activity. Although events of this size are infrequent, there is a significant risk to the communities downstream of the complex.

STABILITY ANALYSIS OF THE SLOPE ALONG US-2 BETWEEN EPOUFETTE BAY AND THE CUT RIVER BRIDGE

Recently, water was observed flowing from a section of steep slope along US-2 near St. Ignace, Michigan in addition to soil sloughing in the area where the water is flowing from the slope. An inspection of the area also showed the presence of sinkholes. The original construction drawing for US-2 also indicated that sinkholes were present in this area prior to road construction in 1948. An investigation was conducted to determine the overall stability of the slope. The slope consists primarily of aeolian sand deposits. Laboratory testing determined the shear strength of the slope material to have a friction angle around 30°, which is also the slope angle. Thus, the slope is at its maximum angle for stability—however, the slope is also heavily wooded which provides additional support to the slope. Although the area surrounding the water flow has been sloughing, the remaining slope remains intact.

STABILITY ANALYSIS AND HAZARD ASSESSMENT OF THE NORTHERN SLOPES OF SAN VICENTE VOLCANO IN CENTRAL EL SALVADOR

Geologic hazards affect the lives of millions of people worldwide every year. El Salvador is a country that is regularly affected by natural disasters, including earthquakes, volcanic eruptions and tropical storms. Additionally, rainfall-induced landslides and debris flows are a major threat to the livelihood of thousands. The San Vicente Volcano in central El Salvador has a recurring and destructive pattern of landslides and debris flows occurring on the northern slopes of the volcano. In recent memory there have been at least seven major destructive debris flows on San Vicente volcano. Despite this problem, there has been no known attempt to study the inherent stability of these volcanic slopes and to determine the thresholds of rainfall that might lead to slope instability. This thesis explores this issue and outlines a suggested method for predicting the likelihood of slope instability during intense rainfall events. The material properties obtained from a field campaign and laboratory testing were used for a 2-D slope stability analysis on a recent landslide on San Vicente volcano. This analysis confirmed that the surface materials of the volcano are highly permeable and have very low shear strength and provided insight into the groundwater table behavior during a rainstorm. The biggest factors on the stability of the slopes were found to be slope geometry, rainfall totals and initial groundwater table location. Using the results from this analysis a stability chart was created that took into account these main factors and provided an estimate of the stability of a slope in various rainfall scenarios. This chart could be used by local authorities in the event of a known extreme rainfall event to help make decisions regarding possible evacuation. Recommendations are given to improve the methodology for future application in other areas as well as in central El Salvador.

Stability boundary analysis of the dynamic voltage restorer in weak systems with dynamic loads

In this contribution, a stability analysis for a dynamic voltage restorer (DVR) connected to a weak ac system containing a dynamic load is presented using continuation techniques and bifurcation theory. The system dynamics are explored through the continuation of periodic solutions of the associated dynamic equations. The switching process in the DVR converter is taken into account to trace the stability regions through a suitable mathematical representation of the DVR converter. The stability regions in the Thevenin equivalent plane are computed. In addition, the stability regions in the control gains space, as well as the contour lines for different Floquet multipliers, are computed. Besides, the DVR converter model employed in this contribution avoids the necessity of developing very complicated iterative map approaches as in the conventional bifurcation analysis of converters. The continuation method and the DVR model can take into account dynamics and nonlinear loads and any network topology since the analysis is carried out directly from the state space equations. The bifurcation approach is shown to be both computationally efficient and robust, since it eliminates the need for numerically critical and long-lasting transient simulations.

Sensitivity analysis by neural networks applied to power systems transient stability

This work presents a procedure for transient stability analysis and preventive control of electric power systems, which is formulated by a multilayer feedforward neural network. The neural network training is realized by using the back-propagation algorithm with fuzzy controller and adaptation of the inclination and translation parameters of the nonlinear function. These procedures provide a faster convergence and more precise results, if compared to the traditional back-propagation algorithm. The adaptation of the training rate is effectuated by using the information of the global error and global error variation. After finishing the training, the neural network is capable of estimating the security margin and the sensitivity analysis. Considering this information, it is possible to develop a method for the realization of the security correction (preventive control) for levels considered appropriate to the system, based on generation reallocation and load shedding. An application for a multimachine power system is presented to illustrate the proposed methodology. (c) 2006 Elsevier B.V. All rights reserved.

Stability and sensitivity analysis of Be-CoDiS, an epidemiological model to predict the spread of human diseases between countries. Validation with data from the 2014-16 West African Ebola Virus Disease epidemic.

Ebola virus disease is a lethal human and primate disease that requires a particular attention from the international health authorities due to important recent outbreaks in some Western African countries and isolated cases in European and North-America continents. Regarding the emergency of this situation, various decision tools, such as mathematical models, were developed to assist the authorities to focus their efforts in important factors to eradicate Ebola. In a previous work, we have proposed an original deterministic spatial-temporal model, called Be-CoDiS (Between-Countries Disease Spread), to study the evolution of human diseases within and between countries by taking into consideration the movement of people between geographical areas. This model was validated by considering numerical experiments regarding the 2014-16 West African Ebola Virus Disease epidemic. In this article, we propose to perform a stability analysis of Be-CoDiS. Our first objective is to study the equilibrium states of simplified versions of this model, limited to the cases of one an two countries, and to determine their basic reproduction ratios. Then, in order to give some recommendations for the allocation of resources used to control the disease, we perform a sensitivity analysis of those basic reproduction ratios regarding the model parameters. Finally, we validate the obtained results by considering numerical experiments based on data from the 2014-16 West African Ebola Virus Disease epidemic.

Power system sensitivity analysis for probabilistic small signal stability assessment in a deregulated environment

Deregulations and market practices in power industry have brought great challenges to the system planning area. In particular, they introduce a variety of uncertainties to system planning. New techniques are required to cope with such uncertainties. As a promising approach, probabilistic methods are attracting more and more attentions by system planners. In small signal stability analysis, generation control parameters play an important role in determining the stability margin. The objective of this paper is to investigate power system state matrix sensitivity characteristics with respect to system parameter uncertainties with analytical and numerical approaches and to identify those parameters have great impact on system eigenvalues, therefore, the system stability properties. Those identified parameter variations need to be investigated with priority. The results can be used to help Regional Transmission Organizations (RTOs) and Independent System Operators (ISOs) perform planning studies under the open access environment.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Power buffer with model predictive control for stability of vehicular power systems with constant power loads

Electrification of vehicular systems has gained increased momentum in recent years with particular attention to constant power loads (CPLs). Since a CPL potentially threatens system stability, stability analysis of hybrid electric vehicle with CPLs becomes necessary. A new power buffer configuration with battery is introduced to mitigate the effect of instability caused by CPLs. Model predictive control (MPC) is applied to regulate the power buffer to decouple source and load dynamics. Moreover, MPC provides an optimal tradeoff between modification of load impedance, variation of dc-link voltage and battery current ripples. This is particularly important during transients or starting of system faults, since battery response is not very fast. Optimal tradeoff becomes even more significant when considering low-cost power buffer without battery. This paper analyzes system models for both voltage swell and voltage dip faults. Furthermore, a dual mode MPC algorithm is implemented in real time offering improved stability. A comprehensive set of experimental results is included to verify the efficacy of the proposed power buffer.

A comparison of stability and bifurcation criteria for inflated spherical elastic shells

The nonlinear stability analysis introduced by Chen and Haughton [1] is employed to study the full nonlinear stability of the non-homogeneous spherically symmetric deformation of an elastic thick-walled sphere. The shell is composed of an arbitrary homogeneous, incompressible elastic material. The stability criterion ultimately requires the solution of a third-order nonlinear ordinary differential equation. Numerical calculations performed for a wide variety of well-known incompressible materials are then compared with existing bifurcation results and are found to be identical. Further analysis and comparison between stability and bifurcation are conducted for the case of thin shells and we prove by direct calculation that the two criteria are identical for all modes and all materials.

Stability synthesis of power hardware-in-the-loop (PHIL) simulation

A virtual power system can be interfaced with a physical system to form a power hardware-in-the-loop (PHIL) simulation. In this scheme, the virtual system can be simulated in a fast parallel processor to provide near real-time outputs, which then can be interfaced to a physical hardware that is called the hardware under test (HuT). Stable operation of the entire system, while maintaining acceptable accuracy, is the main challenge of a PHIL simulation. In this paper, after an extended stability analysis for voltage and current type interfaces, some guidelines are provided to have a stable PHIL simulation. The presented analysis have been evaluated by performing several experimental tests using a Real Time Digital Simulator (RTDS™) and a voltage source converter (VSC). The practical test results are consistent with the proposed analysis.