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PARTICLE FILTERS

As a first application we are focusing on particle filter based prognostics. Particle filtering is a well-known and powerful technique for non-linear state-estimation problems. On-going research has shown great promise for application of particle filters to prognostics. They can be effectively used to track progression of system state in order to make estimations of remaining useful life (RUL), which is at the core of system prognostics and health management.

However, particle filters impose significant demand on computation power and memory resources and are considered good candidates for parallelization and/or distributed implementations. In terms of computation, a particle filter based system essentially consists of the following three computational steps:

  • Sampling: In this step, samples (particles) of the unknown state are generated based on the given sampling function which propagate the particles from the previous time step to the current time and also provide an estimate of the current state of the system.
  • Weight Calculation: Based on the observations, an importance weight is assigned to each particle.
  • Resampling: This step involves redrawing particles from the same probability distribution based on some function of the particle weights such that the weights of the new particles are equal.

In general, all the above steps in the particle filters can be parallelized except for the last step of resampling. Though, various efforts to derive parallelized versions of particle filters have been made, it has not been possible till now to formulate a complete parallel version. Also, since the resampling technique being used is often dictated by the application and system requirements, existing parallel versions cannot be used in all designs.

Several architectures for particle filter based systems have been proposed. An example of a distributed architecture is shown in the following figure. In this figure, the CEs (Computing Elements) perform sampling and weight calculation while the central server performs all the steps in particle filtering. Thus, the steps of sampling and weight calculation in the particle filter are shared amongst the CEs and the central server while the resampling is done solely by the central server after collecting all the updated particle weights from the rest of the CEs.

System architecture for particle filter based prognostics system.

Experiments

Experiments were carried out on a particle-filter based battery health monitoring system where electrochemical impedance spectroscopy (EIS) is used to probe the internal electrochemical reactions of batteries. Particle filtering was used to track internal health parameters followed by predictions for RUL.

The dataset used in the experiments was collected from second generation 18650-size lithium-ion cells (i.e., Gen 2 cells) that were cycle-life tested at the Idaho National Laboratory under the Advanced Technology Development (ATD) program. The dataset was divided into a training set (at 25oC) and a test set (at 45oC). The training set was used to extract features and estimate the internal parameters for the battery. These parameters were then used to initialize the prognosis i.e., RUL (Remaining Useful Life) predictions. RUL predictions were made after tracking the test data for 32 weeks and 48 weeks.

The full system was implemented on Sun SPOT devices. The following two configurations were used:

    2-SPOT: Base station connected to a laptop acting as the central monitor and 1 free-ranging SPOT device.
  • 3-SPOT: Base station connected to a laptop acting as the central monitor and 2 free-ranging SPOT devices.

The following figure shows both the state tracking and future state prediction plots for data collected at 45oC. RUL or TTF (time to failure) is used as the relevant metric for the state-of-life (SOL). This is derived by projecting out the capacity estimates into the future until expected capacity hits a certain predetermined RUL threshold (end-of-life criteria). The particle distribution is used to calculate the RUL probability density function (pdf) by fitting a mixture of Gaussian distributions in a least-squares sense.

Particle Filter Output using 2-SPOT configuration

The RUL pdf improves in both accuracy (centering of the pdf over the actual failure point) and precision (spread of the pdf over time) with the inclusion of more measurements before prediction. The average (over 10 executions) RUL values computed at 32 weeks and 48 weeks for the 2-SPOT configuration are 58.06 weeks and 61.17 weeks respectively, while the corresponding values for the 3-SPOT configuration are 59.93 and 61.99 weeks. The actual failure occurs at 62 weeks. The static program memory usages of the SPOT devices for 2 SPOT and 3 SPOT configurations are as follows:

  • Free range SPOTs: 29KB
  • Base station: 101KB

The decrease in execution time results for the two configurations are shown below.

Execution time result comparison for 2-SPOT and 3-SPOT configurations

Discussion

Since offline sensor data was being used in the experiments, the base station was connected to a laptop using a USB cable. The files containing the sensor information and other initialization information were read through the USB cable and communicated to the free ranging SPOTs appropriately.

The main issue faced in the design was the limitations imposed by the restrictions on the message length by the communication channel; all the state information for a single iteration could not be packed into a single message. Thus, the message had to be broken into multiple parts and sent iteratively both by the base station to send state information to the free ranging SPOT and the free ranging SPOT to communicate updated state information to the base station.

The execution times were obtained by averaging over 10 separate executions of the whole system, since the execution time varies – within a margin of 10-15 ms – mainly based on the wireless communication time which is dependent on the distance between the SPOTs. The execution time decreases for the 3-SPOT configuration compared to the 2-SPOT. However, a significant decrease is not observed due to the resampling step which is serial in nature and is executed completely on the base station. Also, as the number of SPOTs is increased, the amount of time spent on communication increases, which diminishes the effect of the gain in execution time obtained by distributing the computation workload.

The low program memory utilization of the free ranging SPOTs demonstrates that more multitasking can be delegated to them; instead of executing a single application as discussed here, more allocated tasks would enable more efficient use of resources.

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