Subspace estimation and prediction methods for hidden Markov models

Hidden Markov models (HMMs) are probabilistic functions of finite Markov chains, or, put in other words, state space models with finite state space. In this paper, we examine subspace estimation methods for HMMs whose output lies a finite set as well. In particular, we study the geometric structure arising from the nonminimality of the linear state space representation of HMMs, and consistency of a subspace algorithm arising from a certain factorization of the singular value decomposition of the estimated linear prediction matrix. For this algorithm, we show that the estimates of the transition and emission probability matrices are consistent up to a similarity transformation, and that the $m$-step linear predictor computed from the estimated system matrices is consistent, i.e., converges to the true optimal linear $m$-step predictor.Comment: Published in at http://dx.doi.org/10.1214/09-AOS711 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nonparametric estimation of mixing densities for discrete distributions

By a mixture density is meant a density of the form $\pi_{\mu}(\cdot)=\int\pi_{\theta}(\cdot)\times\mu(d\theta)$, where $(\pi_{\theta})_{\theta\in\Theta}$ is a family of probability densities and $\mu$ is a probability measure on $\Theta$. We consider the problem of identifying the unknown part of this model, the mixing distribution $\mu$, from a finite sample of independent observations from $\pi_{\mu}$. Assuming that the mixing distribution has a density function, we wish to estimate this density within appropriate function classes. A general approach is proposed and its scope of application is investigated in the case of discrete distributions. Mixtures of power series distributions are more specifically studied. Standard methods for density estimation, such as kernel estimators, are available in this context, and it has been shown that these methods are rate optimal or almost rate optimal in balls of various smoothness spaces. For instance, these results apply to mixtures of the Poisson distribution parameterized by its mean. Estimators based on orthogonal polynomial sequences have also been proposed and shown to achieve similar rates. The general approach of this paper extends and simplifies such results. For instance, it allows us to prove asymptotic minimax efficiency over certain smoothness classes of the above-mentioned polynomial estimator in the Poisson case. We also study discrete location mixtures, or discrete deconvolution, and mixtures of discrete uniform distributions.Comment: Published at http://dx.doi.org/10.1214/009053605000000381 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Synthesis gas generation by chemical-looping reforming in a continuously operating laboratory reactor

Chemical-looping reforming is a technology that can be used for partial oxidation and steam reforming of hydrocarbon fuels. This paper describes continuous chemical-looping reforming of natural gas in a laboratory reactor consisting of two interconnected fluidized beds. Particles composed of 60 wt% NiO and 40 wt% MgAl2O4 are used as bed material, oxygen carrier and reformer catalyst. There is a continuous circulation of particles between the reactors. In the fuel reactor, the particles are reduced by the fuel, which in turn is partially oxidized to H-2, CO, CO2 and H2O. In the air reactor the reduced oxygen h of reforming were recorded. Formation of solid carbon was noticed for some cases. Adding 25 vol% steam to the natural gas reduced or eliminated the carbon formation

Chemical-Looping Combustion and Chemical-Looping Reforming in a Circulating Fluidized-Bed Reactor Using Ni-Based Oxygen Carriers

Three oxygen carriers for chemical-looping combustion and chemical-looping reforming have been investigated in a small circulating fluidized-bed reactor. N2AM1400 was produced by freeze granulation with MgAl2O4 as a support material and had a NiO content of 20%. Ni18-αAl was produced by impregnation onto α-Al2O3 and had a NiO content of 18%. Ni21-γAl was produced by impregnation onto γ-Al2O3 and had a NiO content of 21%. Over 160 h of operation has been recorded. The conversion of natural gas into products was 96−100% depending on oxygen carrier and experimental conditions. For chemical-looping combustion, N2AM1400 and Ni21-γAl provided poor selectivity toward CO2 and H2O while Ni18-αAl initially showed very high selectivity, which declined as a function of time. For chemical-looping reforming, operating the reactor at the desired process parameters, which was a fuel reactor temperature of 950 °C and an air factor of 0.30, was possible with all of the tested oxygen-carrier materials. When only natural gas was used as fuel, there was significant formation of solid carbon in the fuel reactor for Ni18-αAl and Ni21-γAl. Adding 30% steam or CO2 to the fuel removed or decreased the carbon formation. During the course of the experiments, N2AM1400 and Ni18-αAl retained their physical and chemical structure, while Ni21-γAl displayed a significant reduction in porosity but remained highly reactive

Chemical-looping combustion and chemical-looping reforming of kerosene in a circulating fluidized-bed 300W laboratory reactor

The reaction between a nickel-based oxygen carrier and a liquid fuel has been demonstrated in a chemical-looping reactor with continuous particle circulating. An injection system was constructed, in which sulfur-free kerosene was evaporated, mixed with superheated steam and fed directly into the lab scale chemical-looping reactor. A nickel-based oxygen carrier composed of 40 wt% NiO and 60 wt% MgO-ZrO2 was used for both chemical-looping combustion (CLC) and chemical-looping reforming (CLR) experiments, which were performed for about 34 h and 20 h, respectively. For the CLC experiments, 95-99% of the fuel carbon was converted to CO2 and only a minute amount of hydrocarbons was detected in the off-gas. For the CLR experiments, synthesis gas was produced with concentrations of hydrocarbons as low as 0.01%. The particles were analyzed before and after the experiments using XRD, SEM, BET surface area and particle size distribution. It was shown that it is possible to use liquid fuel in a continuous chemical-looping process and also achieve nearly complete fuel conversion. With a nickel-based oxygen carrier virtually all hydrocarbon could be fully oxidized

Combined oxides as oxygen-carrier material for chemical-looping with oxygen uncoupling

Oxygen-carrier materials for chemical-looping with oxygen uncoupling (CLOU) must be capable of taking up and releasing gas-phase O2 at conditions relevant for generation of heat and power. In principle, the capability of a certain material to do so is determined by its thermodynamic properties. This paper provides an overview of the possibility to design feasible oxygen carrier materials from combined oxides, i.e. oxides with crystal structures that include several different cations. Relevant literature is reviewed and the thermodynamic properties and key characteristics of a few selected combined oxide systems are calculated and compared to experimental data. The general challenges and opportunities of the combined oxide concept are discussed. The focus is on materials with manganese as one of its components and the following families of compounds and solid solutions have been considered: (MnyFe1-y)Ox, (MnySi1-y)Ox, CaMnO3-δ,(NiyMn1-y)Ox, (MnyCu1-y)Ox and (MnyMg1-y)Ox. In addition to showing promise from a thermodynamic point of view, reactivity data from experimental investigations suggests that the rate of O2 release can be high for all systems. Thus these combined oxides could also be very suitable for practical application

Waste products from the steel industry with NiO as additive as oxygen carrier for chemical-looping combustion

Fe2O3-containing waste materials from the steel industry are proposed as oxygen carrier for chemical-looping combustion. Three such materials, red iron oxide, brown iron oxide and iron oxide scales, have been examined by oxidation and reduction experiments in a batch fluidized-bed reactor at temperatures between 800 and 950°C. NiO-based particles have been used as additive, in order to examine if it is possible to utilize the catalytic properties of metallic Ni to facilitate decomposition of hydrocarbons into more reactive combustion intermediates such as CO and H2. The experiments indicated modest reactivity between the waste materials and CH4, which was used as reducing gas. Adding small amounts of NiO-based particles to the sample increased the yield of CO2 in a standard experiment, typically by a factor of 1.5-3.5. The fraction of unconverted fuel typically was reduced by 70-90%. The conversion of CH4 to CO2 was 94% at best, corresponding to a combustion efficiency of 96%. This was achieved using a bed mass corresponding to 57 kg oxygen carrier per MW fuel, of which only 5 wt% was NiO-based synthetic particles. The different materials fared differently well during the experiments. Red iron oxide was fairly stable, while brown iron oxide was soft and subject to considerable erosion. Iron oxide scales experienced increased reactivity and porosity as function of the numbers of reduction cycles

Combined Cu/Mn Oxides as an Oxygen Carrier in Chemical Looping with Oxygen Uncoupling (CLOU)

This study investigates the O2 uncoupling properties of five different oxygen carrier particles, consisting of combined oxides of CuO and Mn3O4. The oxygen carriers were produced by freeze granulation followed by calcination at 950 °C for 6 h. Particles with 5, 10, 20, 31, and 61 wt % CuO were examined in both an inert (pure N2) atmosphere and in the presence of solid fuel (wood char) at 750 °C. At this relatively low temperature during fluidization with N2, the samples were capable of releasing gas-phase O2 in concentrations up to 1%. During reduction with wood char in 15 g of oxygen carriers, some materials could release gaseous O2 equal to 1.4% of their total mass. When the crushing strength and attrition index were measured with a customized jet cup, the mechanical stability of these samples was compared. These measurements showed that, in general, samples with a higher CuO content were more mechanically stable. On the basis of XRD analysis of the oxygen carriers, the major phase transitions were Mn2O3 ↔ Mn3O4 and combined spinel (Cu,Mn)3O4 ↔ CuMnO2. These transitions both provide a considerable amount of O2. It is concluded that the Cu–Mn–O system has considerable potential to be used as a oxygen carrier in chemical-looping applications at lower temperatures, perhaps interesting for biofuel combustion