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EN
Large-scale panel destressing is a rockburst mitigation technique employed in deep hard rock mines during remnant pillar extraction. Panels are choke blasted in the pillar footwall to cutoff the far-field major stress in the mining area and deviate them around the pillar. In this study, the effects of panel geometry and far-field stress magnitude are investigated. Destress blast performance is assessed by measuring change to the energy release rate (ERR) of all mining steps during the extraction of a simplified remnant pillar due to destressing. It is demonstrated that the energy release rate (ERR) of critical stopes is reduced by 30% with the base panel geometry. The panel thickness is shown to have the most influence on the efficiency of destressing, followed by the stand-off distance between the panel and the pillar and the overhang length of the panel. The effect of far-field stress magnitude on the ERR is also investigated, and the destress blast performance is expressed as an equivalent major principal stress reduction. It is shown that with the base panel geometry, the destressing program offers the same ERR reduction as a 9.6 MPa reduction in the far-field stress for the most critical stopes. Finally, the Copper Cliff Mine (CCM) panel destressing program is presented as a case study. The ore at risk and ERR are calculated over the extraction and destressing sequence in the pillar with a pillar-wide numerical model.
EN
This paper investigates the use of iterative linear methods applied to the power flow problem (PFP) solution in power systems. Preconditioning techniques are studied and incorporated to the methodology to solve a linear system. As application to the PFP, four iterative linear techniques and a direct method are evaluated and their performances are compared. Numerical experiments demonstrate the effectiveness of the proposed methodology, suggesting the good performance of the Bi-conjugate Gradient Stabilized (BiCGStab) as an adequate iterative linear method for the applicability in the solution of a PFP.
PL
W artykule analizowano metodę iteracyjną zastosowaną do kontroli przepływów mocy. Zbadano cztery liniowe techniki iteracyjne i metodę bezpośrednią Najlepsze właściwości wykazała technika Bi-conjugated Gradient Stabilized BiCGStab.
EN
Solving many problems in mechanics, engineering, medicine and other (e.g., diffusion tensor magnetic resonance imaging or finite element modeling) requires the efficient solving of algebraic equations. In many cases, such systems are very complex with a large number of linear equations, which are symmetric positive-defined (SPD). This paper is focused on improving the computational efficiency of the solvers dedicated for the linear systems based on incomplete and noisy SPD matrices by using preconditioning technique – Incomplete Cholesky Factorization, and modern set of processor instructions – Advanced Vector Extension. Application of these techniques allows to fairly reduce the computational time, number of iterations of conventional algorithms and improve the speed of calculation.
4
Content available remote Influence of preconditioning and blocking on accuracy in solving Markovian models
EN
The article considers the effectiveness of various methods used to solve systems of linear equations (which emerge while modeling computer networks and systems with Markov chains) and the practical influence of the methods applied on accuracy. The paper considers some hybrids of both direct and iterative methods. Two varieties of the Gauss elimination will be considered as an example of direct methods: the LU factorization method and the WZ factorization method. The Gauss-Seidel iterative method will be discussed. The paper also shows preconditioning (with the use of incomplete Gauss elimination) and dividing the matrix into blocks where blocks are solved applying direct methods. The motivation for such hybrids is a very high condition number (which is bad) for coefficient matrices occuring in Markov chains and, thus, slow convergence of traditional iterative methods. Also, the blocking, preconditioning and merging of both are analysed. The paper presents the impact of linked methods on both the time and accuracy of finding vector probability. The results of an experiment are given for two groups of matrices: those derived from some very abstract Markovian models, and those from a general 2D Markov chain.
PL
Artykuł przedstawia kształtowanie się rzeczywistego stanu zagrożenia tąpaniami oraz zakres stosowanej aktywnej profilaktyki tąpaniowej w parceli ściany 8 zlokalizowanej w północno wschodniej części Obszaru Górniczego "Bytom-Centrum I" KWK "Bobrek-Centrum", w obszarze filara ochronnego miasta Bytom. Pokład 510 w polu ściany 8 zalega na głębokości 550-730 m, z nachyleniem 5-11 stopni w kierunku na południowy zachód; miąższość pokładu wynosi: 9,0-9,7 m. W czasie eksploatacji pokładu 510 ścianą 8 występowały okresy wzmożonej aktywności sejsmicznej. Z uwagi na kształtowanie się zagrożenia tąpaniami, można wydzielić dwa różniące się zasadniczo okresy prowadzenia ściany 8: od uruchomienia ściany do końca września 2007 r. i od października 2007 r. do chwili obecnej, tj, do 7 grudnia 2008. Wypracowana ostatecznie aktywna profilaktyka tąpaniowa w postaci strzelań wstrząsowych i kamufletowych w pokładzie, strzelań torpedujących strop pokładu i wysokociśnieniowego nawadniania calizny pokładu oraz ograniczenia techniczne (postępu dobowego do 2,1 m i wysokości ściany do 2,3 m) pozwoliły na kontynuowanie eksploatacji pokładu 510 ścianą 8. W konsekwencji większość silnych wstrząsów sprowokowana była aktywną profilaktyką tąpaniową, głównie strzelaniami kamufletowymi i kamufletowo-wstrząsowymi. Dużą skutecznością wykazała się też metoda wysokociśnieniowego nawadniania calizny pokładu. Długi okres (do 25 godzin) utrzymywania się ciśnienia wody, stuki, odprężenia i wstrząsy oraz wzrosty emisji sejsmoaustycznej, występujące podczas nawadniania ściany 8 w pokładzie 510 w.d. świadczą o skuteczności tej metody.
EN
The article presents the formation of the real rockburst hazard condition and scope of applied active rockburst prevention on the longwall 8 located in the north-eastern part of the mining Area "Bytom-Centrum I", "Bobrek-Centrum" Colliery, in the safety pillar of the town Bytom. The seam 510 in the panel of longwall 8 occurs at the depth of 550-730 m, with the inclination 5-110 towards south-west; the seam thickness amounts to: 9.0-9.7 m. During longwall 8 mining in the seam 510 occurred periods with enhanced seismic activity. On account of the rockbust hazard formation, two essentially differing periods of longwall 8 mining can be distinguished: from longwall operation start till the end of September 2007 and from October 2007 till the present moment, i.e. till 7 December 2008. The finally worked out active rockburst prevention in the form of shock and camouflet blasting in the seam, torpedo blasting in the roof and high-pressure water injection into the seam coal solid as well as technical limitations (daily advance up to 2.1 m and longwall height up to 2.3 m) allowed to continue longwall 8 mining in the seam 510. In consequence the majority of strong tremors was provoked by active rockburst prevention, mainly camouflet blasting as well as camouflet and preconditioning. High efficiency indicates also the method of high-pressure water injection into the seam coal solid. The long period (up to 25 hours) of maintaining of water pressure, knocks, destressing and tremors as well as seismoacoustics emission increase, occurring during the water injection on longwall 8 in the seam 510, prove the efficiency of this method.
EN
A preconditioned solution scheme for the computation of compressible flow in turbomachinery at arbitrary Mach numbers is presented. The preconditioning technique used is applied to a state-of-the-art explicit, time-marching Navier-Stokes code which originally was developed for compressible, high-speed turbomachinery applications. It combines the ideas of low Mach number preconditioning and artificial compressibility method into a unified approach where principally fluids with arbitrary equations of state can be simulated. As shown by the test cases presented, it allows the code to simulate flows efficiently and accurately independent of the Mach number. A description of the Navier-Stokes equations for rotating coordinate systems, along with the solution scheme and the details of the preconditioning method is given. Since turbomachinery computations are often performed on truncated domains, the solution scheme should be used in conjunction with non-reflecting boundary conditions. A change in the time-dependency of the equations due to preconditioning necessitates a modification of the boundary conditions. Thus, a derivation of the appropriate boundary conditions for the presented preconditioned scheme was performed and the resultant equations are given in this paper. The effectiveness of the new boundary conditions is demonstrated by comparing them with both boundary conditions that use the standard one-dimensional characteristic approach and the original boundary conditions for the non-preconditioned case.
7
Content available remote Iterative Model Reduction of Large State-Space Systems
EN
There exist criteria for reducing the order of a large state-space model based on the accuracy of the approximate solutions to the Lyapunov matrix equations and the Hankel operator. Iterative solution techniques for the Lyapunov equations with the Arnoldi method have been proposed in a number of papers. In this paper we derive error bounds for approximations to the solutions to the Lyapunov equations as well as for the Hankel operator that indicate how to precondition while solving these equations iteratively.These bounds show that the error depends on three terms: First, on the amount of invariance of the constructed subspace for A, second, on the eigenvalues of A at least in proportion to 1/|Re l|, and third, under a certain condition on projectors P_l=W_lW_l* ,on the factor min_{X in C^{l x p}}|| B-( l I-A)W_lX|| for l on a path G surrounding the spectrum of A. Consequently, in order to compensate for those parts of the spectrum where 1/|Re l| is not small, preconditioning or an inverse iteration is needed to keep the sizes of the matrices used in construction of a reduced-order model moderate.
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