Measurement-driven Quality Assessment of Nonlinear Systems by Exponential Replacement

We discuss the problem how to determine the quality of a nonlinear system with respect to a measurement task. Due to amplification, filtering, quantization and internal noise sources physical measurement equipment in general exhibits a nonlinear and random input-to-output behaviour. This usually makes it impossible to accurately describe the underlying statistical system model. When the individual operations are all known and deterministic, one can resort to approximations of the input-to-output function. The problem becomes challenging when the processing chain is not exactly known or contains nonlinear random effects. Then one has to approximate the output distribution in an empirical way. Here we show that by measuring the first two sample moments of an arbitrary set of output transformations in a calibrated setup, the output distribution of the actual system can be approximated by an equivalent exponential family distribution. This method has the property that the resulting approximation of the statistical system model is guaranteed to be pessimistic in an estimation theoretic sense. We show this by proving that an equivalent exponential family distribution in general exhibits a lower Fisher information measure than the original system model. With various examples and a model matching step we demonstrate how this estimation theoretic aspect can be exploited in practice in order to obtain a conservative measurement-driven quality assessment method for nonlinear measurement systems.Comment: IEEE International Instrumentation and Measurement Technology Conference (I2MTC), Taipei, Taiwan, 201

Bayesian inference for stochastic differential equation mixed effects models of a tumor xenography study

We consider Bayesian inference for stochastic differential equation mixed effects models (SDEMEMs) exemplifying tumor response to treatment and regrowth in mice. We produce an extensive study on how a SDEMEM can be fitted using both exact inference based on pseudo-marginal MCMC and approximate inference via Bayesian synthetic likelihoods (BSL). We investigate a two-compartments SDEMEM, these corresponding to the fractions of tumor cells killed by and survived to a treatment, respectively. Case study data considers a tumor xenography study with two treatment groups and one control, each containing 5-8 mice. Results from the case study and from simulations indicate that the SDEMEM is able to reproduce the observed growth patterns and that BSL is a robust tool for inference in SDEMEMs. Finally, we compare the fit of the SDEMEM to a similar ordinary differential equation model. Due to small sample sizes, strong prior information is needed to identify all model parameters in the SDEMEM and it cannot be determined which of the two models is the better in terms of predicting tumor growth curves. In a simulation study we find that with a sample of 17 mice per group BSL is able to identify all model parameters and distinguish treatment groups.Comment: Minor revision: posterior predictive checks for BSL have ben updated (both theory and results). Code on GitHub has ben revised accordingl

Physics-based prognostic modelling of filter clogging phenomena

In industry, contaminant filtration is a common process to achieve a desired level of purification, since contaminants in liquids such as fuel may lead to performance drop and rapid wear propagation. Generally, clogging of filter phenomena is the primary failure mode leading to the replacement or cleansing of filter. Cascading failures and weak performance of the system are the unfortunate outcomes due to a clogged filter. Even though filtration and clogging phenomena and their effects of several observable parameters have been studied for quite some time in the literature, progression of clogging and its use for prognostics purposes have not been addressed yet. In this work, a physics based clogging progression model is presented. The proposed model that bases on a well-known pressure drop equation is able to model three phases of the clogging phenomena, last of which has not been modelled in the literature yet. In addition, the presented model is integrated with particle filters to predict the future clogging levels and to estimate the remaining useful life of fuel filters. The presented model has been implemented on the data collected from an experimental rig in the lab environment. In the rig, pressure drop across the filter, flow rate, and filter mesh images are recorded throughout the accelerated degradation experiments. The presented physics based model has been applied to the data obtained from the rig. The remaining useful lives of the filters used in the experimental rig have been reported in the paper. The results show that the presented methodology provides significantly accurate and precise prognostic results

A Data-Driven Predictive Model of Reliability Estimation Using State-Space Stochastic Degradation Model

The concept of the Industrial Internet of Things (IIoT) provides the foundation to apply data-driven methodologies. The data-driven predictive models of reliability estimation can become a major tool in increasing the life of assets, lowering capital cost, and reducing operating and maintenance costs. Classical models of reliability assessment mainly rely on lifetime data. Failure data may not be easily obtainable for highly reliable assets. Furthermore, the collected historical lifetime data may not be able to accurately describe the behavior of the asset in a unique application or environment. Therefore, it is not an optimal approach anymore to conduct a reliability estimation based on classical models. Fortunately, most of the industrial assets have performance characteristics whose degradation or decay over the operating time can be related to their reliability estimates. The application of the degradation methods has been recently increasing due to their ability to keep track of the dynamic conditions of the system over time. The main purpose of this study is to develop a data-driven predictive model of reliability assessment based on real-time data using a state-space stochastic degradation model to predict the critical time for initiating maintenance actions in order to enhance the value and prolonging the life of assets. The new degradation model developed in this thesis is introducing a new mapping function for the General Path Model based on series of Gamma Processes degradation models in the state-space environment by considering Poisson distributed weights for each of the Gamma processes. The application of the developed algorithm is illustrated for the distributed electrical systems as a generic use case. A data-driven algorithm is developed in order to estimate the parameters of the new degradation model. Once the estimates of the parameters are available, distribution of the failure time, time-dependent distribution of the degradation, and reliability based on the current estimate of the degradation can be obtained