An Expectation Maximization Algorithm to Model Failure Times by Continuous-Time Markov Chains

In many applications, the failure rate function may present a bathtub shape curve. In this paper, an expectation maximization algorithm is proposed to construct a suitable continuous-time Markov chain which models the failure time data by the first time reaching the absorbing state. Assume that a system is described by methods of supplementary variables, the device of stage, and so on. Given a data set, the maximum likelihood estimators of the initial distribution and the infinitesimal transition rates of the Markov chain can be obtained by our novel algorithm. Suppose that there are m transient states in the system and that there are n failure time data. The devised algorithm only needs to compute the exponential of m×m upper triangular matrices for O(nm2) times in each iteration. Finally, the algorithm is applied to two real data sets, which indicates the practicality and efficiency of our algorithm

Comparison of Fluid Flow and Temperature Distribution in a Single-Strand Tundish with Different Flow Control Devices

The effects of flow control devices (FCD) in a single-strand tundish, including weir, dam, turbulence inhibitor and gas curtain, have been investigated using water model experiments and CFD simulations. A scaled-down water model was built up to visualize flow pattern and measure the residence-time distribution (RTD) of different tundish configurations. A CFD model was applied to calculate the fluid flow, heat transfer and RTD curves in the prototype tundish under the nonisothermal conditions. The Eulerian–Lagrangian approach was applied to investigate the bubble flow in the system. The results show that each FCD has its own unique function to control the flow. It is important to evaluate the combined effects of FCD based on their installations. The molten steel flow in the tundish could be improved if these flow control devices were arranged properly

A Prediction Model for Internal Cracks during Slab Continuous Casting

Slab continuous casting internal cracking is a common quality defect in the production process. The ability to predict the quality of each continuous casting product and assess whether it is suitable for hot delivery or needs to be cleaned down will greatly increase the rolled product rate and reduce the scrap rate and production management cost. According to the quality defects of internal cracks during slab continuous casting and based on the solidification and heat transfer simulations, stress and strain calculations and theoretical analysis of metallurgical processes related to continuous casting combined with an abnormal casting event expert system, the internal crack generation index of the slice unit is used to predict the crack occurrence rating of each sized slab. Moreover, the internal crack prediction model for the slab is successfully developed and applied in a domestic steel mill. The accuracy of the model prediction reached 86.85%. This method achieved the organic combination of theoretical analysis and an expert system and provides an important theoretical tool for the prediction of crack quality defects in slab continuous casting; the method can be applied in slab continuous casting production

An Approach for Modelling Slag Infiltration and Heat Transfer in Continuous Casting Mold for High Mn–High Al Steel

To clarify the characteristics of slag infiltration and heat transfer behaviors in the meniscus region during the casting of high Mn–high Al steel, a mathematical model of a continuous casting mold that couples fluid flow with heat transfer, and solidification is developed. The model is based on the change in slag composition and properties caused by the steel/slag reaction. The formation and evolution of the meniscus profile and slag films for different mold fluxes during mold oscillation are described. The results show that the rapid growth of the slag rim with a high Al2O3 content approaches and deforms the meniscus so that a series of casting problems such as slag infiltration blocking, large fluctuations in heat flux, and even meniscus breaking occur in the continuous casting process. Predictions are in good agreement with plant measurements. These findings provide an improved understanding of the complex phenomena occurring in the meniscus region and give new insights into the evaluation and optimization of mold flux properties for high Mn–high Al steel casting

Interface analysis and hot deformation behaviour of a novel laminated composite with high-Cr cast iron and low carbon steel prepared by hot compression bonding

A hot compression bonding process was developed to prepare a novel laminated composite consisting of high-Cr cast iron (HCCI) as the inner layer and low carbon steel (LCS) as the outer layers on a Gleeble 3500 thermomechanical simulator at a temperature of 950 °C and a strain rate of 0.001 S-1. Interfacial bond quality and hot deformation behaviour of the laminate were studied by microstructural characterisation and mechanical tests. Experimental results show that the metallurgical bond between the constituent metals was achieved under the proposed bonding conditions without discernible defects and the formation of interlayer or intermetallic layer along the interface. The interfacial bond quality is excellent since no deterioration occurred around the interface which was deformed by Vickers indentation and compression test at room temperature with parallel loading to the interface. After well cladding by the LCS, the brittle HCCI can be severely deformed (about 57 % of reduction) at high temperature with crack-free. This significant improvement should be attributed to the decrease of crack sensitivity due to stress relief by soft claddings and enhanced flow property of the HCCI by simultaneous deformation with the LCS

Parameter Estimation of a Multistate Model for an Aging Piece of Equipment under Condition-Based Maintenance

We study a multistate model for an aging piece of equipment under condition-based maintenance and apply an expectation maximization algorithm to obtain maximum likelihood estimates of the model parameters. Because of the monitoring discontinuity, we cannot observe any state's duration. The observation consists of the equipment's state at an inspection or right after a repair. Based on a proper construction of stochastic processes involved in the model, calculation of some probabilities and expectations becomes tractable. Using these probabilities and expectations, we can apply an expectation maximization algorithm to estimate the parameters in the model. We carry out simulation studies to test the accuracy and the efficiency of the algorithm

Migration and Enrichment Behaviors of Ca and Mg Elements during Cooling and Crystallization of Boron-Bearing Titanium Slag Melt

Synthetic rutile was prepared from titanium slag melt with low energy consumption and a small amount of additive (B2O3) in our previous work. The modification mechanism of titanium slag was not clear enough. The migration and enrichment behaviors of Ca and Mg elements during cooling and crystallization of boron-bearing titanium slag melt were characterized by XRF, FESEM, EMPA, and XPS. Results show that when additive (B2O3) is added, Ti elements are migrated and enriched in the area to generate rutile, while Ca, Mg, and B elements are migrated and enriched in another area to generate borate. With the additive (B2O3) amount increased, Ca and Mg element migration is complete and more thorough. Additive (B2O3) promotes rutile formation and inhibits the formation of anosovite during cooling and crystallization of titanium slag melt. With the additive (B2O3) amount increasing from 0% to 6%, the proportion of Ti3+ in the modified titanium slag reduces from 9.15% to 0%, and the proportion of Ti4+ increases from 90.85% to 100% under the same cooling and crystallization condition. The result will lay the foundation for the efficient preparation of synthetic rutile by adding B2O3 to the titanium slag melt

Prediction model for crack sensitive temperature region and phase fractions of slab under continuous casting cooling rates based on finite number of experiments

Accurate prediction of the crack sensitive temperature region and phase fractions variation of slabs during continuous cooling is an important guide to avoid cracks and effectively control the quality. Based on finite number of measurements, at different cooling rates of the continuous casting process, a prediction model for characteristic temperatures of austenite decomposition, the variation of phase fractions with temperature, the crack sensitive temperature regions, and the final microstructural compositions of casting slabs at different cooling rates has been established and evaluated the accuracy. The results show that austenite decomposition temperature range moves toward the low temperature region as cooling rate increases, and the independent peak of ferrite transition become weaker. The characteristic temperatures of austenite decomposition can be quantitatively calculated by TC(CR) = A−exp(B + C/CR) at different cooling rates, which the maximum relative error for experimental steels is −2.2%. The ferrite and pearlite phase fractions increases with decreasing temperature during continuous casting cooling, which means that the ability of the billet to resist deformation and external force changes. Meanwhile, the final ferrite content of slabs for Steel B and Steel C at different cooling rates are 83.24620−exp(2.59364–13.72283/CR) and 85.07143−exp(1.71320–15.82244/CR), respectively. The crack sensitive temperature region Ae3 ∼ Tα40%(CR) calculated by the prediction model is in good agreement with the low ductility zone measured by experiment. Moreover, the critical temperatures Tα40%(CR) of the crack sensitive temperature regions are 890.35731−exp(2.99719–20.67781/CR), 745.87462−exp(4.83056–44.18511/CR) and 729.46168−exp(2.96621–12.21949/CR) for three experimental steels under different cooling rates

Phase Transition of Peritectic Steel Q345 and Its Effect on the Equilibrium Partition Coefficients of Solutes

The solidification path of peritectic steel Q345 was calculated and compared with in-situ observations to investigate the effect of phase transition on the equilibrium partition coefficient. Subsequently, a thermodynamic model for calculating the equilibrium partition coefficient was established and thermodynamic calculations were performed under different phase configurations. Results indicate that L (liquid phase) + δ, L + δ + γ, and L + δ phases coexist in sequence during the solidification of peritectic steel Q345. The phase constitution of the mushy zone evidently affects the evolution of the equilibrium partition coefficient of solutes. The temperature dependence of the equilibrium partition coefficient was quantified through the regression analyses of C, Si, Mn, P, and S solutes under different phase configurations. The average equilibrium partition coefficients of Mn, Si, P, C, and S are 0.696, 0.615, 0.273, 0.2, and 0.033, respectively, thereby indicating the strongest segregation tendency for S and the weakest for Mn

Corrosion Resistance of MgO-C Refractory to Smelting Reduction Slag Containing Titania

Interactions between smelting reduction slags containing titania (0.2-20 wt-%TiO2) and MgO-C refractories have been investigated by stationary immersion and rotary immersion at temperatures of 1773-1923 K. The relationship between the concentration of TiO2 in the slag and the corrosion rate of the refractories, the effects of slag basicity (CaO/SiO2), and the effect of the temperature of the molten bath on the corrosion rate were examined. Increasing the TiO2 concentration in the slag caused an increase in the corrosion rate of the MgO-C refractories. The corrosion rate also increased when the temperature was increased. Increasing the basicity of the acid slag decreased the corrosion rate, but this effect was not evident when the basicity of slag exceeded 1.0. The corrosion mechanism of MgO-C refractories in smelting reduction melts containing titania involves the oxidation of graphitic carbon by TiO2 and the formation of a deterioration layer containing Ti and TiC, together with the reaction of matrix MgO with slag to form MgAl2O4, MgCaSiO4, and MgSiO3