We review basic modeling approaches for failure and mainte- nance data from repairable systems. In particular we consider imperfect re- pair models, defined in terms of virtual age processes, and the trend-renewal process which extends the nonhomogeneous Poisson process and the renewal process. In the case where several systems of the same kind are observed, we show how observed covariates and unobserved heterogeneity can be included in the models. We also consider various approaches to trend testing. Modern reliability data bases usually contain information on the type of failure, the type of maintenance and so forth in addition to the failure times themselves. Basing our work on recent literature we present a framework where the ob- served events are modeled as marked point processes, with marks labeling the types of events. Throughout the paper the emphasis is more on modeling than on statistical inference.

On the statistical modeling and analysis of repairable systems

I: Phenomena in the Blast Furnace.- 1 Dissection of Quenched Blast Furnaces.- 1.1 Introduction.- 1.1.1 Background to the present study.- 1.1.2 Methods of quenching and their effects.- 1.1.3 General in-furnace situations and peculiar phenomena.- 1.2 Relation Between Behavior of Descending Burden and State of Combustion Zone.- 1.2.1 Fundamental descent behavior of burden in the shaft.- 1.2.2 Asymmetrical descent of burden.- 1.3 Behavior of the Core.- 1.4 Situations in and Around the Combustion Zone.- 1.4.1 State in front of the tuyere nose.- 1.4.2 Formation of shell and movements at the lower part of the raceway.- 1.4.3 Conditions inside the furnace and the shape of the raceway.- 1.5 Shape of Cohesion Zone and Relation to Distribution and Movement of Burden.- 1.5.1 Formation of the cohesion zone.- 1.5.2 Relation between shape of the cohesion zone and operation conditions.- 1.6 Behavior of Circulating Elements.- 1.6.1 Effect of water quenching on the circulating elements.- 1.6.2 Behavior of circulating elements and amounts of circulation.- 1.7 Changes in Properties of Burden Materials.- 1.7.1 Macroscopic changes.- 1.7.2 Microscopic structural and composition changes.- 1.7.3 Effects of circulating elements on the behavior of the cohesion zone.- 1.8 Reactions in the Hearth.- 1.8.1 Slag formation reactions.- 1.8.2 Changes in the metal composition.- 1.9 Concluding Remarks.- 1.10 Addendum.- 1.10.1 Arrangement inside the furnace.- 1.10.2 Changes in properties of the burden.- 2 Measurements in Operating Blast Furnaces.- 2.1 Objectives of Blast Furnace Measurements.- 2.2 Development of Measurements for Clarification of Furnace Reactions.- 2.2.1 Standard instrumentation for blast furnaces a decade ago.- 2.2.2 Development of instrumentation since the introduction of blast furnace dissection.- 2.3 Relationship Between Furnace Measurement and Furnace Operation (Actual Examples).- 2.3.1 Relationship between measurements before blowing out of blast furnace and results of dissection.- 2.3.2 Measurements and estimations of the cohesive zone.- 2.3.3 Development and use of the latest sensors to study furnace interiors.- 2.4 Future Development of Blast Furnace Measurements.- II: Modelling of the Blast Furnace.- 3 Global Formulation.- 3.1 Review of Blast Furnace Models.- 3.1.1 Reichardt diagram.- 3.1.2 Operation diagram.- 3.1.3 Kinetic model.- 3.1.4 Control models.- 3.1.5 Models for estimating internal situations based on observed data.- 3.2 One-dimensional Static Model.- 3.2.1 Overall reaction rates.- 3.2.2 Overall material balance.- 3.2.3 Temperatures of gas and solid at the top of the furnace.- 3.2.4 Flow rate and composition of gas at tuyere level.- 3.2.5 Theoretical flame temperature.- 3.2.6 Temperature of gas and coke at tuyere level.- 3.2.7 One-dimensional mathematical formulation for internal state of blast furnace.- 3.2.8 Effect of various operating conditions on productivity and situation in blast furnace.- 3.2.9 Some applications of the model.- 3.3 Layered Structure Model.- 3.3.1 Radial distribution of flow rate of gas.- 3.3.2 Mathematical-kinetic model of blast furnace.- 3.3.3 Numerical analysis of blast furnace operation.- 3.3.4 Computed results.- 3.3.5 Steady-state two-dimensional modelling.- 3.3.6 Governing equations for cylindrical polar coordinates.- 3.3.7 Some auxiliary relations.- 3.3.8 Numerical solution of two-dimensional model.- 3.4 Two-dimensional Model for Gas Flow, Heat Transfer and Chemical Reactions.- 3.4.1 General concept of the radial distribution model.- 3.4.2 Momentum transfer.- 3.4.3 Mass transfer with chemical reactions.- 3.4.4 Heat transfer.- 3.4.5 Input conditions.- 3.4.6 Method of analysis.- 3.4.7 Simulation results.- 3.5 Two-dimensional Formulation by Finite Element Method.- 3.5.1 Flow analysis of gas.- 3.5.2 Computed results for gas flow.- 3.5.3 Simultaneous analysis of gas flow and heat transfer.- 3.5.4 Computed results on the simultaneous gas flow and heat transfer.- 3.6 Model for Estimating the Profile of the Cohesive Zone.- 3.6.1 General description of the mathematical model.- 3.6.2 Relation between indices estimated using the mathematical model and from blast furnace operation (cohesive zone analysis with 4000 m3 class blast furnace).- 3.6.3 Analysis of operation with decrease in production.- 3.6.4 Future direction.- 3.7 One-dimensional Dynamic Model.- 3.7.1 Outline of mathematical simulation model.- 3.7.2 Applications to blast furnace operations.- 3.8 Notation.- 4 Flow of Gas, Liquid and Solid.- 4.1 Flow of Solids During Charging and Control of Burden Distribution.- 4.1.1 Burden distribution of bell top furnaces.- 4.1.2 Burden distribution of bell-less top furnaces.- 4.2 Flow of Solids in the Upper Part of the Furnace.- 4.2.1 Information from dissected blast furnaces.- 4.2.2 Burden descent model.- 4.2.3 Decrease in angle of layer inclination with burden descent.- 4.2.4 Influence of some other factors.- 4.3 Flow of Solids in the Lower Part of the Furnace.- 4.3.1 Basic phenomena.- 4.3.2 Formation of mixed zone in the peripheral region near the wall.- 4.3.3 Movement of coke to the raceway.- 4.3.4 Movement of coke in dead coke zone and hearth.- 4.4 Theoretical Approach to the Flow of Burden Material in the Furnace.- 4.4.1 Stress distribution in the blast furnace.- 4.4.2 Inclination of the dead coke zone boundary.- 4.4.3 Notation (Sections 4.3 and 4.4).- 4.5 Numerical Simulation of Radial Gas Flow Distribution.- 4.5.1 Burden distribution model.- 4.5.2 Two-dimensional gas flow in the blast furnace.- 4.5.3 Outline of results of calculation.- 4.5.4 Concluding remarks.- 4.5.5 Notation.- 4.6 Flow of Gas and Liquid in the Dropping Zone.- 4.6.1 Counter-current flow region.- 4.6.2 Cross flow region.- 4.6.3 Concluding remarks.- 4.7 Flow of Slag and Metal in the Hearth During Tapping.- 4.7.1 State of coke bed in the hearth.- 4.7.2 Flow of slag during tapping.- 4.7.3 Flow of metal during tapping.- 4.7.4 Mathematical simulation of hearth flow.- 4.7.5 Concluding remarks.- 5 High Temperature Properties of Iron Ore Agglomerates.- 5.1 Reduction Behavior in Lumpy Zone.- 5.1.1 Estimation of reducibility in lumpy zone.- 5.1.2 Determination of reaction rate constant of reduction and comparison with blast furnace operation.- 5.2 Change of Mineral Phases in Blast Furnace.- 5.2.1 Change of mineral phases during reduction.- 5.2.2 Mineral phases in reduced iron ore agglomerates.- 5.2.3 Change of gangue minerals.- 5.3 Flow Resistance of Gas Through the Fused Packed Bed.- 5.3.1 Measurement of pressure drop in fused packed bed.- 5.3.2 Numerical calculation of gas flow resistance through a fused packed bed by use of an orifice model.- 5.3.3 Equation of pressure drop in fused packed bed.- 5.3.4 Quantitative determination of softening properties.- 5.4 Effects of High Temperature Properties of Burden on Blast Furnace Operation.- 5.4.1 Factors for evaluating high temperature properties of burden.- 5.4.2 Relationship between high temperature properties of burden and blast furnace operating performance.- 5.5 High Temperature Properties of Burden with Cohesive Zone Model and Direct Measurement of Cohesive Zone.- 5.5.1 Estimation of cohesive zone with theoretical models.- 5.5.2 Effect of softening properties on gas permeability.- 5.5.3 Evaluation of softening properties of sinter.- 5.5.4 Direct measurement of cohesive zone.- 5.6 Notation.- 6 The Raceway.- 6.1 Measurement and Observation of the Blast Furnace Raceway.- 6.1.1 Movement of coke particles in the raceway.- 6.1.2 Condition near the raceway.- 6.1.3 Reactions in the raceway.- 6.2 Mathematical Model of the Raceway.- 6.2.1 One-dimensional model.- 6.2.2 Two-dimensional model.- 6.3 Notation.- 7 The Lower Region of the Blast Furnace and the Slag-Metal-Gas Reaction.- 7.1 Reaction of Silicon.- 7.1.1 Introduction.- 7.1.2 Behavior of silicon in the blast furnace.- 7.1.3 Kinetics of silicon transfer.- 7.2 Other Reactions.- 7.2.1 Manganese.- 7.2.2 Titanium.- 7.3 Application of Reaction Models of Silicon to Blast Furnace Operation.- 7.3.1 Review of silicon reaction models.- 7.3.2 Partition reactions of Si, S and Mn.- 7.3.3 Mathematical model of silicon reactions in the blast furnace.- 7.4 Notation.- III: Flexibility and Adaptability of Blast Furnace.- 8 Blast Furnace Ironmaking Technology in the Near Future.- 8.1 Flexible Operation.- 8.2 Increase of Furnace Life.- 8.3 Mechanization of Cast-house Operation.- 8.4 Technology Development Related to Innovative Steelmaking Process.- 8.5 Use of Blast Furnace for Producing Other Metals.

Blast furnace phenomena and modelling

Combined effect of flux and welding parameters on chemical composition and mechanical properties of submerged arc weld metal

It poses a great challenge to control the blast furnace system, often meaning to control the components of the hot metal within acceptable boundary, such as the silicon content in hot metal. For this reason, this paper focuses on addressing the multiclass classification problem about the silicon change in hope of providing reasonable blast furnace control guidance. Through the proposed binary coding support vector machine (SVM) algorithm, a four-class problem, i.e., sharp descent, slight descent, sharp ascent, and slight ascent of the silicon content in hot metal, is reduced into two binary classification problems to solve. To heel, the confidence level about these classification results is also estimated. Reliable classification effect plus very few binary classifiers make the binary coding SVMs full of competitive power for practical applications, particularly when the confidence level is high. The four-class classification results can indicate not only the silicon change direction but also the rough silicon change amplitude, which can guide the blast furnace operators to determine the blast furnace control span together with the control direction in advance.

Binary Coding SVMs for the Multiclass Problem of Blast Furnace System

Investigation of TiO2–SiO2–CaO–CaF2 based electrode coatings on weld metal chemistry and mechanical behaviour of bimetallic welds

The prediction model has been developed for low carbon steel weld metal acicular ferrite microstructure as a function of flux ingredients such as CaO, MgO, CaF 2 and Al 2 O 3 in submerged arc welding carried out at fixed welding parameters. The results of quantitative measurements of acicular ferrite (AF) on eighteen no. of weld metal samples were utilised for developing the prediction model. Among the flux ingredients, CaO appears to be most important as an individual as well as interaction with other ingredients in controlling the amount of acicular ferrite content in the weld metal. Furthermore, formation of acicular ferrite is also related to the weld bead geometry which is influenced by flux ingredients. The prediction equation for acicular ferrite has been checked for adequacy by performing separate experiments on welding using randomly designed flux. The'isoresponse curves were developed to show the level of acicular ferrite content at different percentage of flux ingredients.

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Prediction of Acicular Ferrite from Flux Ingredients in Submerged Arc Weld Metal of C-Mn Steel

The transfer of elements across the molten weld pool has been predicted by developing quadratic models in terms of flux ingredients with the application of statistical experiments for mixture design. Bead-on-plate weld deposits were made at fixed welding parameters using submerged are welding fluxes prepared as per extreme vertices algorithm of mixture experiments in a CaO-MgO-Caf 2 -Al 2 O; flux system. The results show that some of the individual flux ingredients and their binary mixtures have a predominant effect on weld metal transfer of oxygen, manganese, silicon, and carbon contents. The analysis of experimental data also indicates that transfer of oxygen is affected by several properties of flux ingredients such as oxygen potential, thermodynamic stahility, and viscosity. In the element transfer of silicon, both thermochemical and electrochemical reaction mechanisms operate simultaneously. Transfer of manganese is principally related to the weld metal oxygen contents as well as electrochemical reaction in the molten weld pool. The transfer of carbon was generally governed by the oxidation reaction. Iso-response contour plots were also developed to quantify the transfer of elements against different flux compositions.

Prediction of element transfer in submerged arc welding

A prediction model has been developed for submerged arc weld-metal chemical composition in terms of flux ingredients with the help of statistical experiments for mixture (extreme vertices design). Bead-on-plate weld deposits as per statistical mixture design experiments were performed at the following welding parameters: current (400 A), voltage (26 V), speed (4.65 mm/s) and electrode extension (30 mm) using CaO-MgO-CaF 2 -Al 2 O 3 flux system. The results show that some of the individual flux ingredients and their binary mixtures have a predominant effect on weld-metal oxygen, manganese, silicon, sulphur, nickel and carbon content. The predicted results show a reasonably good agreement with the experimental results, which were obtained by performing the actual experiments based on a randomly designed flux. Analysis of the experimental data indicate that several mechanisms such as basicity index, oxygen potential, oxide stability, viscosity, electrode chemical reaction, kinetics of slag-metal reaction, etc. are operating simultaneously to yield the final weld-metal composition.

Prediction of submerged arc weld‐metal composition from flux ingredients with the help of statistical design of mixture experiment

The prediction model has been developed for steel weld metal mechanical properties as a function of flux ingredients such as CaO, MgO, CaF2 and Al2O3 in submerged arc welding carried out at fixed w...

Sujit Kumar Majumdar

Papers

Combined effect of flux and welding parameters on chemical composition and mechanical properties of submerged arc weld metal

Prediction of Acicular Ferrite from Flux Ingredients in Submerged Arc Weld Metal of C-Mn Steel

Prediction of element transfer in submerged arc welding

Prediction of submerged arc weld‐metal composition from flux ingredients with the help of statistical design of mixture experiment

Prediction of Mechanical Properties in Submerged Arc Weld Metal of C–Mn Steel