Search

With rising market deployment the condition monitoring of solid oxide fuel cell systems is gaining particular importance. The conventional approaches mainly use electrochemical impedance spectroscopy based on the repeated sinusoidal perturbation over a range of frequencies. One of the notable weaknesses of the approach is excessively long perturbation time needed to properly evaluate the impedance curve. In this paper, we propose a time-efficient approach in which, a short, persistently exciting and small-amplitude perturbation is used to excite all the relevant system eigenmodes. A model structure from a class of linear fractional order models is selected to describe the perturbed dynamics and to account for anomalous diffusion processes in the cells. Then, the model parameters are estimated directly from measured input and output records. The paper presents a computationally efficient parameter estimation procedure in which the numerical issues of differentiation of noisy signals are alleviated by using modulating functions. In practice, that means a combination of filtering and application of conventional least squares. The approach is applied on a case of health assessment of solid oxide fuel cells.

While high performance of SOFC systems has already been achieved, there is still a need to increase the stack lifetime, while decreasing the system's total cost of ownership, both being linked. The increase in lifetime includes the minimization of performance degradation, but also avoidance of potentially detrimental events during operation, originating from the stack, outside the stack, or a combination of both. The present paper highlights how the detection of faulty operation as early as possible is important to implement adequate mitigation strategies, wherever applicable, according to the fault and its grade of severity. Three types of faults have been considered, fuel starvation, leakage and carbon deposition. Both hardware components and algorithms to monitor, detect, isolate, and finally correct faulty system operation have been developed and will be embedded in a real SOFC system.

Maintaining a high fuel-to-electricity conversion efficiency over a long period of time is important for successful market deployment of SOFC power systems. The conventional control solutions usually do not suffice to reach this goal. In order to properly handle variable load conditions and to mitigate degradation processes, on-line optimization is needed to adjust the process variables and to run the process as close as possible to the operational optimum. In this paper, a supervisory controller is proposed to optimize the operation of the SOFC power system. The outputs of the supervisory controller are references for the low-level controllers. The optimization is solved by means of the extremum-seeking approach where optimum is sought directly on the process. The main advantage is that the model of the process is not needed. The supervisory controller is assessed on a detailed physical model of a 2.5 kW SOFC power system at different load conditions. Simulation results show that the supervisory controller is capable to improve electrical efficiency and keep the system temperatures within the safe ranges. Consequently, degradation processes associated with the thermal stress of the stack are reduced. Due to the slow dynamics of the stack thermal processes, the convergence rate of the supervisory controller is rather slow. The proposed supervisory controller is thus appropriate for SOFC power systems that operate at constant load conditions over long periods of time.

Higher exploitation of fuel cell technologies can be achieved employing effective maintenance and condition monitoring tools. Electrochemical impedance spectroscopy (EIS) is a common way for state-of-health characterisation of fuel cells. However, parameters of an equivalent circuit model (ECM) used to describe the EIS seem to be more convenient and informative. Usually, an ECM structure is selected a priori, and an optimisation problem is formulated to fit the parameters of the model and gain their corresponding point estimates. However, for more precise reasoning, better information about the parameters is desirable. This can be achieved through Bayesian inference. In this paper, Bayesian inference is employed to estimate model parameters and so to obtain the posterior marginal density functions of the model’s parameters. It is shown how point estimates may be misleading. The approach is demonstrated on solid oxide fuel cell (SOFC) short stack.

One of the main challenges for wide-spread utilization of the solid oxide fuel cell (SOFC) power systems is how to achieve high electrical efficiency without increasing the degradation rate of the fuel cells. To run the SOFC power system at high efficiency over a long period of time, properly designed controllers are indispensable. Although a number of various approaches to control SOFC have been proposed so far, it seems that the design of control system, along with simple tuning procedure, has not been treated in a consistent manner. This issue is addressed in the present paper resulting in a feedforward-feedback control structure. The feedforward part is based on the stoichiometry of electro-oxidation, reforming and combustion reactions, which allow immediate response to variable current demand. The feedback part performs additional fine adjustment of fuel and air supply in order to minimize the undesired system temperatures variations. The selection of pairings of manipulated and controlled variables for control is based on physical knowledge of the system. Input/output pairing for single-loop feedback control is assessed by the relative gain analysis. An efficient procedure for tuning the parameters of the feedback controllers is suggested, relying on simple open-loop step responses of the system. The proposed low-level control is assessed on a detailed physical model of a 2.5 kW SOFC power system by simulating two nonstationary load regimes. Simulations show that the control provides a robust operation under large load variations while meeting the operating constraints. Due to its simplicity, the control is feasible for implementation on a real SOFC system.

Solid-oxide fuel cells (SOFCs) represent a group of electrochemical conversion devices that utilise hydrogen rich fuels and are characterised by their high efficiency of energy conversion. For optimal exploitation of SOFCs, accurate and online state-of-health (SoH) assessment is of utmost importance. SoH assessment is usually performed through the frequency domain analysis by characterising the changes of the Nyqvist curves, a process also known as electrochemical impedance spectroscopy. Such an approach is time consuming and suffers from low accuracy particularly at low frequencies. Methodologies for time-domain identification of fractional-order systems offer a way of resolving these issues. Using an algebraic approach to identification, the complete fractional-order transfer function is identified from a series of several step responses. The SoH can be estimated from the identified parameters of the fractional-order transfer function either in a form of a Nyqvist curve or by directly linking particular parameter values to electrochemical processes. The proposed approach was validated on a 300 W SOFC using pure hydrogen fuel.

Operation of the SOFC power system can be improved by upgrading the low-level controllers with a supervisory controller (see Figure 1). In this work a simple, model-free supervisory optimizer that adjusts references for the low level controllers is proposed. The optimization problem for the SOFC power system is formulated with the cost function depending on the electrical efficiency of the system and deviations of the system temperatures from their limits. Electrical efficiency is calculated as the ratio of the net electrical power to the total power obtained by burning the fuel. The dominant parasitic losses of the system are assumed to be mainly related to the air blower consumption. Based on efficiency analysis, which demands a number of simulations on SOFC power system model, the references for the burner lambda and stack outlet and inlet air temperatures are selected as optimization variables. The optimization problem is solved by using the extremum-seeking approach where optimum is sought directly on the process. An advantage of this approach is that it does not need a model of the system and exceeds the weakness of model-based optimizers, which assume nominal process condition all the time and do not take into account the degradation processes in fuel cells. Its disadvantage is it needs to probe the system at all time by imposing small variations on manipulated variables and delivers a convergence speed which is somewhat slower compared to the model based approach. A simple algorithm is designed to perform the model-free optimization. The algorithm is additionally augmented to incorporate changes in the current load in order to increase the convergence speed of the optimization at large load changes. The efficiency of the optimizer is governed by properly tuned parameters of the optimization algorithm. Proposed supervisory optimizer is assessed on a simulated detailed physical model of a 2.5 kW SOFC power system by applying large step current load changes. Simulation results indicate that the optimizer improves efficiency of the system by approximately 10 % compared to the low-level controllers and keeps the system temperatures within the safe ranges (see Figure 2). Due to its simplicity the optimizer appears appropriate for practical applications. Figure 1

Having concurrent information regarding the state of health (SoH) of an operating solid oxide fuel cell (SOFC) stack can actively improve its overall management. Firstly, operating the SOFC by taking into account current health conditions, and its anticipated trend, can be beneficial to the total life span of the stack. Furthermore, such information can be of great importance to the maintenance staff, e.g. unplanned shutdowns can be avoided. Relatively little work has been done in the field of remaining useful life (RUL) prediction of SOFCs. The majority of work employs stack/cell voltage as a direct link for RUL predictions. This paper proposes an integrated approach for SoH estimation based on stack’s Ohmic area specific resistance (ASR). Subsequently, a drift model that describes the ASR increase over time enables accurate RUL prediction. The approach consists of three steps. Firstly, an Unscented Kalman filter, based on a lumped stack model, estimates the current ASR value. Secondly, a drift model for describing the temporal evolution in ASR is recursively identified employing the linear Kalman filter. Finally, employing the identified drift model, Monte Carlo simulation is performed to predict future time evolution in ASR and so to obtain RUL. The developed approach is validated with experimental data from a 10 kW SOFC power system. The results confirm that ASR is a viable SoH indicator for the SOFC stack.

Degradation and poisoning of solid oxide fuel cell (SOFC) stacks are continuously shortening the lifespan of SOFC systems. Poisoning mechanisms, such as carbon deposition, form a coating layer, hence rapidly decreasing the efficiency of the fuel cells. Gas composition of inlet gases is known to have great impact on the rate of coke formation. Therefore, monitoring of these variables can be of great benefit for overall management of SOFCs. Although measuring the gas composition of the gas stream is feasible, it is too costly for commercial applications. This paper proposes three distinct approaches for the design of gas composition estimators of an SOFC system in anode off-gas recycle configuration which are (i.) accurate, and (ii.) easy to implement on a programmable logic controller. Firstly, a classical approach is briefly revisited and problems related to implementation complexity are discussed. Secondly, the model is simplified and adapted for easy implementation. Further, an alternative data-driven approach for gas composition estimation is developed. Finally, a hybrid estimator employing experimental data and 1st-principles is proposed. Despite the structural simplicity of the estimators, the experimental validation shows a high precision for all of the approaches. Experimental validation is performed on a 10 kW SOFC system.

Accurate prediction of the remaining useful life (RUL) of machines is becoming mandatory in exploiting the asset in an efficient and secure way by avoiding the unplanned downtimes. In this paper we present an approach to the RUL prediction developed for a shot blasting machine by analyzing the recordings from inexpensive vibrational sensors. The key idea consists of (i) employing generalized Jensen-Renyi divergence (JRD) as a measure of change in the vibrational pattern (ii) exploiting the monotone relationship between JRD and the abrasive wear in rotor blades and (iii) using a Markov model to describe wear dynamics. The unknown parameters of the Markov model are obtained by expectation-maximization approach. Prediction of the remaining useful life is done by executing Monte Carlo simulations on the updated model and evaluation of the first passage time of the JRD index. The approach is validated experimentally by running the machine up to the failure, hence allowing for naturally evolving wear progression.

Understanding the way in which the degradation of a system's component is coupled to the system's dynamics is highly relevant for the monitoring and control of modern engineering systems. This paper focuses on the identification of coupling functions that describe the relationship between the system's dynamics and the degradation rate in solid-oxide fuel cell (SOFC) stacks. Based on the degradation dynamics estimated from data acquired online, we can design timely mitigation actions as well as optimal maintenance interventions. We introduce a computationally tractable identification approach that takes into account prior knowledge of the form of the coupling function that is found experimentally for a certain degradation mechanism. The nonlinear coupling function is estimated using variational Bayesian inference. The approach is tested on a 1600 h recording from a SOFC system. It is shown that the use of the prior form of the coupling function results in a superior prediction of the degradation, when compared with that obtained using purely data-driven black-box models. The reliable convergence of the variational Bayesian method and the simplicity of its implementation make it a promising tool for the in-field performance monitoring of SOFC systems. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

Distributed bearing faults appear under various circumstances, for example due to electroerosion or the progression of localized faults. Bearings with distributed faults tend to generate more complex vibration patterns than those with localized faults. Despite the frequent occurrence of such faults, their diagnosis has attracted limited attention. This paper examines a method for the diagnosis of distributed bearing faults employing vibration analysis. The vibrational patterns generated are modeled by incorporating the geometrical imperfections of the bearing components. Comparing envelope spectra of vibration signals shows that one can distinguish between localized and distributed faults. Furthermore, a diagnostic procedure for the detection of distributed faults is proposed. This is evaluated on several bearings with naturally born distributed faults, which are compared with fault-free bearings and bearings with localized faults. It is shown experimentally that features extracted from vibrations in fault-free, localized and distributed fault conditions form clearly separable clusters, thus enabling diagnosis.

The solid oxide fuel cells (SOFCs) represent a promising technology for sustainable power generation from hydrogen rich fuels with high efficiency of energy conversion. However, only a limited number of papers address the problem of on-line maximisation of the efficiency of SOFC operation. Optimal operating conditions are normally chosen either based on experience or by using elaborated models, which are not easy to obtain. Moreover, the process changes over time due to degradation, hence the model-based performance optimisation requires on-line model update. To avoid these problems, a model-free approach is proposed. It is realised in the form of a two-tier control structure where the low-level controllers take over control of the auxiliary units around the fuel cells, while the supervisory controller (SC) controller optimises the operation point of the system. The low-level controllers are conventional feed-forward feed-back controllers, while optimisation on the higher level is solved by using the extremum seeking approach. The proposed control system is demonstrated on a simulated 10 kW SOFC system showing reliable convergence, relative rise of efficiency up to 2% and easy design and maintenance.

Standard approaches to the diagnostic decision making require prior knowledge about the diagnosed process and data records at various faulty conditions. This is not easy to meet in practice. In this paper we propose a data-driven non-parametric approach to fault detection and isolation, which relies on evaluating the dissimilarity statistic feature evaluated from current measurement records and features taken during the nominal fault-free machine condition. For that purpose the Jensen-Renyi divergence of the empirical distributions is employed. Hence the need for data records at different failure modes is avoided. The approach has been initially developed for robust bearing diagnostics and is presented here in that context. It has been validated on simulated and experimental case studies with bearings faults. Moreover, the approach is rather general and applicable in a number of other domains as well.

Smooth and timely control actions improve the efficiency and durability of solid oxide fuel cell (SOFC) power systems. In this paper a systematic feedforward-feedback approach to control design for SOFC power systems is proposed. The control aim is to regulate the temperature of and the temperature difference over the stack by manipulating the air flow, air inlet temperature and fuel flow. The feedforward part responds to the demanded electrical current and stoichometry of reforming and electrochemical processes. It gives the fuel flow rate needed to achieve the required stack current with a given fuel utilization. The air flow rate is then calculated according to the oxygen consumption in fuel cells and a given air utilization. Feedforward control is combined with the feedback control to adjust the manipulated variables based on the measured system output. Relative gain array (RGA) analysis (Shinskey, 1988) is performed over the system inputs and outputs (I/O) to determine optimal I/O pairing for control. The RGA is calculated from the static gain matrix of the SOFC stack model (Sorrentino et al., 2008). The strongest interactions are found between the cathode outlet temperature and the cathode inlet temperature, the stack temperature difference and the air flow rate, and the stack voltage and the fuel flow rate. Fuel flow rate has a strong influence also on the stack temperature and can be in some situations used to support temperature control. Based on the RGA analysis, two individual PI control loops are determined. In the first loop, the cathode outlet temperature is controlled by the proportional-integral (PI) controller that uses the cathode inlet temperature as the manipulated variable. In the second loop, the stack temperature difference is controlled by the PI controller with the air flow rate as the manipulated variable (see Figure 1). Altogether the control system consists of two PI control loops, making it feasible for practical implementation. The control target is similar as in (Pohjoranta et al., 2015) but it is obtained here with a significantly simpler approach. Anti-windup protection is included in the PI controllers to avoid long settling times caused by the limits on the manipulated variables (Peng et al, 1999). Parameters of the PI controllers are tuned from the open-loop step response experiments by applying the Magnitude Optimum Multiple Integration (MOMI) method (Vranèiæ et al., 1999). The feedforward-feedback control is evaluated on the SOFC stack model (Sorrentino et al., 2008) over a one-day operation cycle using the standard load profile of residential houses (Knight and Ribbering, 2007). The proposed feedforward-feedback control provides good control of the stack temperatures (see Figure 2). Relatively high stack voltage changes are caused by the significant load changes, however, but these can be reduced by combining a SOFC power system with an energy buffer. References Knight, I., Ribbering, H. (eds.) (2007). European and Canadian non-HYAC Electric and DHW Load Profiles for Use in Simulating the Performance of Residential Cogeneration Systems. A Report of Subtask A of FC+COGEN-SIM: The Simulation of Building-Integrated Fuel Cell and Other Cogeneration Systems. Peng Y., Vrancic D., Hanus R. (1996). Anti-windup, bumpless, and conditioned transfer techniques for PID controllers. Control syst. mag., 16, 48-57. Pohjoranta, A., Halinen, M., Pennanen, J., Kiviaho, J. (2015). Model predictive control of the solid oxide fuel cell stack temperature with models based on experimental data. Journal of Power Sources, 277, 239-250. Shinskey, F.G. (1988). Process control systems. 3rdedition. McGraw-Hill, New York. Sorrentino, M., Pianese, C., Guezennec, Y.G. (2008). A hierarchical modeling approach to the simulation and control of planar solid oxide fuel cells. Journal of Power Sources, 180, 380-392. Vrancic, D., Peng, Y., Strmcnik, S. (1999). A new PID controller tuning method based on multiple integrations, Control Engineering Practice, 7(5), 623-633. Figure 1

Accurate estimation of the remaining useful life (RUL) of a machine can have significant operational and financial benefits for the companies. The biggest challenge in the remaining useful life (RUL) estimation are features that exhibit monotonic behaviour correlated with the level of deterioration of the machine’s condition. This is particularly challenging under variable operating conditions. The proposed RUL estimation approach is based on characterising the energy distribution of vibration signals. The features hereupon quantify the departure from the initial healthy state by calculating the f-divergence measures. Then the divergence measure is modelled as the output of a hidden Markov process in state space. In the general case, the states of the nonlinear model are estimated by means of unscented Kalman filter. Future evolution of the states and the outputs can be evaluated by Monte Carlo simulations. Hereupon, one can evaluate the distribution of times at which the calculated output hits the limit value marking the end of operability. The approach was applied to the problem of monitoring the turbine of a milling machine. The experiment was designed as a run-to-failure test thus allowing the natural progression of the mechanical fault.

Imperfections in process models, if ignored, may affect reliability of the diagnostic system, for example through excessive false alarm rates. The problem tackled in this paper is how to handle unmodelled effects, caused by imperfect nominal models. We propose a covariance model, which builds on the idea that bias in nominal model can be described by a stochastic process. The Gaussian process model is used to capture the discrepancy between reality and nominal model, hence resulting in a refined model of the plant. With unmodelled dynamics as a second-order stochastic process, fault detection problem reduces to the problem of statistical decision making. The onset of a fault is inferred by comparing the statistical pattern of the residuals, collected under current operating mode with the pattern in the nominal (fault-free) condition. Major novelty of the approach resides in employing Jensen-Renyi divergence as a means to express the "distance" between the two corresponding ensembles of distributions. The ideas of the approach and their potentials are demonstrated on a simulated solid oxide fuel cell system.

Thermal stress is one of the main factors affecting the degradation rate of solid oxide fuel cell (SOFC) stacks. In order to mitigate the possibility of fatal thermal stress, stack temperatures and the corresponding thermal gradients need to be continuously controlled during operation. Due to the fact that in future commercial applications the use of temperature sensors embedded within the stack is impractical, the use of estimators appears to be a viable option. In this paper we present an efficient and consistent approach to data-driven design of the estimator for maximum and minimum stack temperatures intended (i) to be of high precision, (ii) to be simple to implement on conventional platforms like programmable logic controllers, and (iii) to maintain reliability in spite of degradation processes. By careful application of subspace identification, supported by physical arguments, we derive a simple estimator structure capable of producing estimates with 3% error irrespective of the evolving stack degradation. The degradation drift is handled without any explicit modelling. The approach is experimentally validated on a 10 kW SOFC system.

Reliable fault diagnosis of mechanical drives can become nontrivial task in case of restricted instrumentation and variable operating conditions. Under such circumstances changes in the calculated features can not be unambiguously associated with change in system condition. In this paper we propose a feature appropriate for diagnosing faults in mechanical drives that is robust to fluctuations in operating conditions. Therefore, its time evolution seems to be correlated only with the machine condition. Instead of relying on spectral properties of the vibration signal, we rather observe changes in the statistical patterns of the derived distribution functions. The effectiveness of the algorithm was evaluated on three datasets comprising both gear and bearing faults under constant and variable load.

The lifespan of a solid oxide fuel cell (SOFC) stack depends on several factors, such as the internal stack temperature and temperature gradients as well as the fuel gas oxygen-to-carbon (O/C) ratio within the stack. An excessively high stack operating temperature generally accelerates degradation processes while large temperature gradients over the stack increase the thermal stress within the stack which may lead to the delamination of repeating unit components. A too low O/C ratio inflicts carbon deposition which quickly leads to stack breakage. Therefore, monitoring these variables is of vital importance. Although measuring temperatures within the stack and measuring the fuel gas composition at the stack inlet is feasible, this raises the overall equipment cost. In this paper a data-driven design of soft sensors for stack minimum and maximum temperatures as well as the O/C ratio at the anode and pre-reformer inlet is presented. For temperature estimation both dynamic and static models are derived and their performance is compared. The dynamic model is identified using subspace identification, which results in a causal state-space model. The non-causal static model assumes that a combination of process variables at the stack inlet and outlet describe its internal condition. The estimation of gas composition at the inlets, which is required for O/C ratio estimation, is based solely on static relationships. The soft sensors are designed in such a way that adding extra inputs yields no further increase in estimate accuracy. The empirical data required for modelling were obtained from a complete SOFC power generation unit. The results show that estimates of all the relevant variables can be accomplished by simple linear regression models. Keywords: SOFC, soft sensor, O/C estimation, temperature estimation Figure 1

Improvement in efficiency and reliability are essential for more intensive deployment and exploitation of solid oxide fuel cell (SOFC) systems in modern society. Having the information about current health, degradation rate, and estimated remaining useful life (RUL) of the stack, at all times during operation, can greatly benefit the control system performance. Such information can be beneficial also for the service providers and end-users as the maintenance needs, including stack replacements, can be planned in advance. The control system can be able to optimize performance through a trade-off between maximal life span and best efficiency of power conversion. The knowledge on health status and its anticipated evolution assures easy and cost-effective maintainability. However, works that address issue of RUL prediction for SOFC are scant. On top of that, most of authors define voltage as health index and predict RUL accordingly. Such a selection of health index becomes inappropriate when SOFC is working under varying load conditions. In such a case stack voltage becomes affected by the changes in operating conditions and it is difficult to correlate drop in voltage with degradation rate. In this paper, we propose a novel hybrid approach to RUL prediction of SOFC systems, which overcomes the limitations of the known approaches and allows for reliable RUL prediction in non-stationary operating conditions. The approach consists of three main modules: (i.) estimation of area specific resistance (ASR) of the stack, (ii.) prediction of its future progress based on collected data, and (iii.) prediction of RUL. The methodology is evaluated on a 6 kW SOFC system. Figure 1

In condition monitoring (CM) of mechanical drives, the analysis of various physical and chemical properties of the operating lubricant can be used to diagnose defects and assess the state of the system. Recent developments in on-line oil condition sensors and advances in signal processing methods have allowed for a system for on-line oil analysis to be developed and applied in the field of predictive maintenance. The System for On-line Oil Analysis (SOOA) has the ability to measure multiple oil properties of interest and detect faults induced by transients in the acquired signals. Transient detection is based on the cumulative sum of errors (CUSUM) technique, where the error represents the difference between the predicted reference value and the current measured value. Detection of abnormal behaviour, based on transient detection, is followed by fault diagnosis, through integrated assessment of oil properties in real time. The system can operate as a standalone unit with an independent user interface or as a part of a complete integrated diagnostic system, merging oil condition evaluation with vibrational analysis and other techniques. This paper focuses on the algorithms within SOOA in charge of transient detection and fault diagnosis. The results of SOOA operation are presented through a demonstration of the method in a laboratory environment with two different sets of tests: gear pitting and water contamination.