This section summarizes the results of the project. Periodic updates were spread by Newsletter.

For details on the results presented in this page you may download the papers listed in the “Scientific Publications” page (click here then on the conference or journal links), the presentations given at the DIAMOND Workshop held on December 16, 2016 (click here then on workshop agenda) and the presentations available in the “Presentations” page (click here).


The project DIAMOND tackles the problem of monitoring, diagnosing and controlling (MDC) SOFC systems with a holistic approach to achieve advanced management. The close link among these three functions guarantees a comprehensive solution to the problem of achieving improved performance, maintenance scheduling, higher reliability and thus increased lifetime. The key innovation of the project consists in the coupling  between diagnosis and control (i.e. the main management tasks) through condition monitoring, which supports the other two functions.


The project focuses on two SOFC based CHP units; one being an integrated module (HotBox™) with two stacks, heat exchangers and reformer and an external BoP controlling the gases supply, the total power of such a system is 2 kW; the second one is a single stack of 10 kW connected to an external BoP with conventional layout. These two distinct configurations cover a broad spectrum of possible SOFC system assemblies, e.g. multi-stack, medium power generator, integrated fuel processor and components. It’s worth to note that both configurations have not received yet the proper attention towards the integration of monitoring, diagnosis and control to improve their performance. Below the two systems on the laboratories for the experimental campaign.

DIAMOND-C 10 kW System DIAMOND-A 2 kW System

Model development

A comprehensive mathematical tool was designed and developed to simulate the DIAMOND-C system. In the figure, the scheme on the left summarizes the interactions among experimental data and monitoring models implemented per each component of the SOFC system. The complete description of the dynamic model and its validation phase is reported into the publication ECS Transactions 68: 3095-3106 listed in the section Scientific Publication. The reliability of the proposed approach for model-based diagnostic tool was demonstrated via separate validation of each sub-model (e.g. stack, pre-heater, external reformer etc.) as well as through complete transient simulations. The figure on the right show the comparison between experimental data and the simulation results for two model configurations.

Scheme1 ResultsUNISA-1
Monitoring model development process Stack cathode outlet temperature simulated

The DIAMOND-C system model was, then improved upon the new data delivered by VTT, with the installation of the new Elcogen® stacks. Non-linear electrochemical processes have been modelled by means of look-up tables and multi-variable regressions preserving acceptable physical adherence with respect to the modelled phenomena. Once completed all system model and diagnostic equations reduction, the obtained algorithm has been properly coded for PLC operation. The coding process was performed in tight collaboration between UNISA and INEA.

The models library developed for DIAMOND-C has been adapted to simulate the DIAMOND-A system equipped  with an integrated stack module, a lumped dynamic model is now available for DIAMOND-A system (HoTbox). Many efforts have been spent to model the heat exchange among system components in order to consider their strong thermal interaction. Heat exchange is evaluated assuming the outlet temperature as the state variable of each component, considering also materials, system layout and geometrical data. Preliminary results have confirmed the validity of the model-based approach proposed for advanced control and diagnostic strategies development. In the image below the rendering of the modeled module with one stack (top left) and the heat flows among the module inner components (bottom left); on the right the main variables simulated for a step current transient (top right plot).


The model allows simulating with a good accuracy all system components with a maximum relative error of about 4% and 5% in dynamic and steady-state conditions. The comparison between measured and simulated stack voltage shows a good model accuracy with a maximum relative error lower than 2%. The comparison between measured and simulated temperatures indicates a relative error lower than 5% with respect to cathode outlet temperature, and lower than 3% about the anode.

Further results are shown in the figure below for the HoTbox, whose scheme is reported together with the plots of the main variables during a current step-up and step-down transient. The modeling analysis underlines the sensivity of heat exchanges among system components in order to reach steady-state conditions inside the HoTbox. Moreover, heat exchange is influenced in a nonlinear way by the system layout. This represents a critical point in the design of control and diagnostic strategies and requires accurate sub-models. System thermal state influences methane conversion level in the pre-reformer (as shown in the figure below), which must be controlled in order to keep system efficiency high and avoid critical operating conditions for the SOFC stack.  Temperatures and methane conversion factor of pre-reformer are in agreement with experimental data.


Diagnostic tool

DIAMOND diagnostics is developed for integrated stack modules (DIAMOND-A) and conventional systems (DIAMOND-C), all approaches start from the results of previous projects GENIUS and DESIGN funded by FP7-FCH-JU. During GENIUS several approaches were tested, in DIAMOND model-based ones are enhanced for conventional systems and applied to advanced configurations, namely ISM. The signal-based approach implemented in DESIGN for stack faults and degradation detection is also applied in DIAMOND together with other techniques being tested, among others, total harmonic distortion (THD) approach has been positively evaluated for fuel starvation.

The model-based diagnostic approach implemented by DIAMOND serves to detect and isolate faults occurring in both systems (C and A) at stack and balance of plant levels. Results on the DIAMOND modeling and diagnostics developments confirm earlier stack leakage analyses carried out on the DIAMOND-C system stack.

To detect and isolate the faults occurring in the balance of plant a series of fault trees has been developed by applying a fault tree analysis (FTA). They will serve as basis for the implementation of the fault signature matrix to be embedded into the diagnostic tool. The figure below reports an example of fault tree developed to detect faults in air heat exchanger (figure below).

Total harmonic distortion approach is being used on small size SOFC Single Repeating Unit (SRU) and stack. This low cost technique already used for PEMFC diagnostics is promising for detecting critical cell and stack operation status, such as fuel or air starvation, from the stack sum voltage only. The response of SRU and stack by using THD is studied as a function of AC amplitude, frequency and operating point. It has been seen that the range of frequency to be studied for the detection of fuel starvation is between 1 and 0.01 Hz to useful detect mass transport limitations. In the figure below,  the detection of Fuel Utilization FU>80% is clearly detected with THD by applying a 10% AC amplitude. Moreover, THD has been transposed on a 25-cells stack instrumented with 25 cell voltage measurements. It appears that detection of fault like high FU will be more accurate with mean value of THD than mean value of cell voltage measurements.

Fault Tree Analysis (FTA) Total Harmonic Distortion (THD)

Modification to the Fault Detection and Isolation (FDI) algorithm is the subject of the second half of the project. This activity deals wit the enhancement of isolation procedure, based on Fault Signature Matrix, bringing thus the diagnostic algorithm from laboratory environment to real applications. As a result the reduction in the symptoms available for fault isolation occurs with the merging of some faults in clusters, hindering univocal fault isolation. To avoid this occurrence, several model setups (e.g. inverse or isolated component sub-models) have been investigated to increase symptoms number and consequently improve fault isolability. Fault simulations are under analysis to establish a further link with DIAMOND-C testing.

The proposed advanced framework (click on the block scheme to enlarge), within which the final diagnostic algorithm is developed, uses, on the one hand, the Fault Tree Analysis (FTA) approach as a basis for the definition of a heuristic Fault Signature Matrix (FSM), then improved via fault simulation through the complete SOFC system model. On the other hand, to improve fault isolability, the introduction of isolated sub-models approach allows overcoming the main limitations given by the reduction in sensors availability when facing on-field applications. The whole diagnostic algorithm, made of system and component models as well as detection and isolation logics, undergoes mathematical complexity reduction process aiming at both control design and on-board (i.e. PLC) implementation.

The advancements introduced by the application of the isolated sub-models approach consists in residuals redundancy increase, since with the same inputs and variables the number of residuals depends on the model used to compute them (click on figure to enlarge).

advanceddiagnosticframework isolatedsubmodels
Complete diagnostic scheme  Application of the isolated sub-models approach

As an example, the reported FSM shows the achievement of univocal isolation of a fault in the stack from that of the heat exchanger (HEX) by addition of the adjoint residuals (green side) to the conventional ones (blue side).


Another diagnostic strategy developed along the DIAMOND project is based on signal analysis in the frequency domain. It focused on degradation phenomena that occur progressively and continuously, without causing instantaneous irreversible damage but very dangerous in the long term. It is based on the comparison of measured data with respect to the typical (i.e., expected) behaviour of SOFC systems in the frequency domain. In order to detect degrading signatures, a spectral estimation procedure has been developed to describe the distribution (over frequency) of the power contained in a signal, based on a finite set of data, and to detect signals buried in wideband noise.

Control tool

One of the objectives of the controllers to be implemented for SOFC power systems is to improve their efficiency and durability. To this aim, the feedforward-feedback controllers to ensure fast load tracking were designed. The feedforward part of the controller reacts to the electrical current demand as well as the stoichiometry of electro-oxidation. Feedback part performs corrections of the controlled system output by additional manipulation of system inputs. Parameters of the feedback controllers were tuned from the open-loop step response experiments. Important hidden variables such as stack temperatures and fuel composition, that should be under control, are estimated on-line and used by control system. Stack temperatures are estimated from available sensor readings, while a combination of stoichiometry and data is used to estimate fuel composition. The soft sensors build on static mapping of available sensors like flows, temperatures and electric quantities. The designed feedforward-feedback controllers and soft sensors are computationally extremely simple and can be easily implemented in practice. The figure below reports the reference feedforward-feedback control scheme.

Operation of the SOFC power system can be improved by upgrading the low-level controllers with a supervisory optimizer. A simple, model-free supervisory optimizer for SOFC power systems was designed. The optimizer adjusts set-points for the low level controllers in a way to maximize electrical efficiency of the system and prevent stack voltage drops. The optimization problem is solved by using the extremum-seeking approach where optimum is sought directly on the process. The optimizer is robust to discrepancy between the model and system and can be easily implemented in practice. It shows good performance and exceeds the weakness of model-based optimizers, which assume nominal process condition all the time and do not take into account the degradation process. In the picture below the control scheme proposed.

Low-level feedforward-feedback control scheme ControlScheme
Feedforward-feedback control scheme Control scheme proposed

Low-level controllers, first extensively verified in a simulation environment, were implemented on the DIAMOND-A system. The controllers were tested remotely through the INEA PLC, DIAMOND-A system PLC, PC, and data server. The implemented control system consists of four feedforward controllers and two PI control loops. Parameters of the PI controllers were tuned for open-loop step response experiments. Performance of the controllers was verified by applying step load changes. Experimental results show that the proposed controllers provide robust operation under load variations (figure below).

picture1 picture2
Scheme of the implemented low-level control Experimental validation of the low-level controllers

Supervisory optimizer

Supervisory optimizer is implemented on the detailed physical model of the 2.5 kW SOFC Hotbox power system in the gPROMS environment. The optimizer adjusts references for the low-level controllers to maximise the electrical efficiency of the system while satisfying a number of constraints. The optimization problem is solved by using the extremum-seeking approach where optimum is sought directly on the process. Supervisory optimizer improves the electrical efficiency of the system by approximately 10% compared to the efficiency of the system controlled by low-level controllers. It also keeps the system temperatures in the safe ranges. Due to its simplicity, the optimizer appears appropriate for practical applications.

The figures below show the supervisory control scheme of the 2.5 kW SOFC Hotbox power system and the results obtained with a conventional strategy (left bottom) and with the proposed supervisory optimizer (right bottom).

supervisorycontrol supervisorycontrol
Supervisory control scheme Results obtained on DIAMOND-A

The supervisory control module was tested on the DIAMOND-C system and implemented on a standard PLC. It consists of several modules as shown in below. The low-level controllers took care of keeping the operating flows and temperatures at the prescribed reference values. The controllers were tuned solely based on simple step responses. The supervisory module was in charge of solving a constrained optimization problem where various instances of the criterion function included electrical efficiency and/or degradation rate. In the experiment carried out on site, the objective of the supervisor was to minimize the degradation rate of the cells by manipulating the stack outlet air temperature. In spite of short duration of the experiment, caused by to rapid deterioration of the stack, the proposed supervisory control system (figure below) returned promising initial results.

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Supervisory control strategy Experimental validation for DIAMOND-C

Prediction of the remaining useful life of SOFC’s stack

Among the objectives of DIAMOND, the direct and indirect improvement of the stack & system lifetime is one of the long term target. Estimation of the remaining lifetime estimate is tackled to consolidate modeling approaches as a first step towards the development of prognostics tools. For practical purposes it is worth to recall that the problem of estimating the remaining useful life (RUL) of SOFC’s stacks is twofold. First, the information about RUL is central in predictive maintenance of the deployed devices. Second, it can help the control system in accommodating the control strategies in order to extend the achievable lifespan.

A three-step procedure for RUL prognosis is proposed. In the first step, the ohmic area specific resistance (ASR) of the stack is estimated. In the second step, a hidden Markov model of the evolution of ASR over time is identified from available on-line data. Finally, this model is used to evaluate the feasible ASR trajectories and, consequently, the distribution of first passage times through the critical value of ASR. The experimental validation is performed on an excerpt of the experimental data from the 10 kW SOFC power system.

The figure below reports on the experimental validation of the RUL algorithm proposed. The plot contains three elements: experimental (true) RUL, contours of the RUL probability distribution  pRUL(tRUL), which is defined on tRUL and mode (the most likely value) of the corresponding RUL distribution. On the right image the RUL prediction is shown.

rul-plot c9e5bb22-93b7-4167-89c8-263bb146bd05
Experimental validation RUL prediction

Evaluation of Diagnostic and Control Tools at System Level

The algorithms developed in the first two years of the project will be tested on the two CHP systems being studied in DIAMOND, as described in the introduction. The activity planned for both DIAMOND-A  (i.e. HoTbox module) and DIAMOND-C (i.e. conventional) systems has started after M18. As part of the test plan, also general guidelines for data acquisition were created to best support signal-based system diagnostics as well as the identification of models for diagnostics and control. The first testing phases of the DIAMOND-A system included (1) an “iron-plant” experiment carried out with a dummy-stack and (2) the nominal operation experiments with the real stack module; factorial experiment designs are applied to elaborate the most significant input-output dependencies as well as interactions in the system.

A preliminary validation on experimental data measured on the DIAMOND-C system configuration was performed, achieving stack leakage isolation. Then that system was revamped by substituting the single 10 kW stack (see picture on the top) with two 3 kW stacks, equaling an electric output of 6 kW. In the figure below one of the two stacks and the BOP on the back. The stack was built at VTT and designed in co-operation by VTT and ELCOGEN. The new arrangement for DIAMOND-C requires some further refinements of the monitoring model to guarantee the proper accuracy for diagnostic and control algorithms development.