Fuzzy Kalman Filter Validation Using the Local Statistical Approach

Rigatou²,

Djida

2015

MBE

A method for early diagnosis of parametric changes in intracellular protein synthesis models (e.g. the p53 protein - mdm2 inhibitor model) is developed with the use of a nonlinear Kalman Filtering approach (Derivative-free nonlinear Kalman Filter) and of statistical change detection methods. The intracellular protein synthesis dynamic model is described by a set of coupled nonlinear differential equations. It is shown that such a dynamical system satisfies differential flatness properties and this allows to transform it, through a change of variables (diffeomorphism), to the so-called linear canonical form. For the linearized equivalent of the dynamical system, state estimation can be performed using the Kalman Filter recursion. Moreover, by applying an inverse transformation based on the previous diffeomorphism it becomes also possible to obtain estimates of the state variables of the initial nonlinear model. By comparing the output of the Kalman Filter (which is assumed to correspond to the undistorted dynamical model) with measurements obtained from the monitored protein synthesis system, a sequence of differences (residuals) is obtained. The statistical processing of the residuals with the use of x2 change detection tests, can provide indication within specific confidence intervals about parametric changes in the considered biological system and consequently indications about the appearance of specific diseases (e.g. malignancies).

Section: State Estimation Using the Derivative-free Nonlinear Kalman ...mentioning

confidence: 99%

Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering

Rigatou²,

Djida

2015

MBE

“…(9), with the specific choice of parameter values, is accurate. To this end, the following normalized error square (NES) is defined [33] = −1 (27) The normalized error square follows a 2 distribution. An appropriate test for the normalized error sum is to numerically show that the following condition is met within a level of confidence (according to the properties of the 2 distribution)…”

Section: B Consistency Checking Of the Option Pricing Modelmentioning

confidence: 99%

“…It can be noticed, that in case of parametric changes and deviation from the nominal parameter values the residuals' sequence (differences between the real option prices and the ones predicted by the Derivative-free nonlinear Kalman Filter) has clearly a non-zero mean value. A more advanced processing of the residuals sequence can be [30][31][32][33].…”

Section: B Detection Of Mispricing In the Energy Pricing Modelmentioning

confidence: 99%

A Kalman filtering approach to the detection of option mispricing in electric power markets

2014 IEEE Symposium on Computational Intelligence Applications in Smart Grid (CIASG)

2014

Option pricing models are usually described with the use of stochastic differential equations and diffusion-type partial differential equations (e.g. Black-Scholes models). In case of electric power markets these models are complemented with integral terms which describe the effects of jumps and changes in the diffusion process and which are associated with variations in the production rates, condition of the transmission and distribution system, pay-off capability, etc. Considering the latter case, that is a partial integrodifferential equation for the option's price, a new filtering method is developed for estimating option prices variations without knowledge of initial conditions. The proposed filtering method is the so-called Derivative-free nonlinear Kalman Filter and is based on a transformation of the initial option price dynamics into a state-space model of the linear canonical form. The transformation is shown to be in accordance to differential flatness theory and finally provides a model of the option price dynamics for which state estimation is possible by applying the standard Kalman Filter recursion. Based on the provided state estimate, validation of the Black-Scholes partial integrodifferential equation can be performed and the existence of inconsistent parameters in the electricity market pricing model can be concluded.

“…Otherwise, a failure can be detected [8][9][10]. Moreover by applying the χ 2 tests in subsections of the monitored system, the faulty components of it can be also isolated [11][12].…”

Section: Introductionmentioning

confidence: 99%

Fault diagnosis in multi-machine power systems using the Derivative-free nonlinear Kalman Filter

2016 IEEE Workshop on Environmental, Energy, and Structural Monitoring Systems (EESMS)

Siano

Wira

et al. 2016

In this paper a new approach to parametric change detection and failure diagnosis for interconnected power units is proposed. The method is based on a new nonlinear filtering scheme under the name Derivative-free nonlinear Kalman Filter and on statistical processing of the obtained state estimates, according to the properties of the χ2 distribution. To apply this fault diagnosis method, first it is shown that the dynamic model of the distributed interconnected power generators is a differentially flat one. Next, by exploiting differential flatness properties a change of variables (diffeomorphism) is applied to the power system, which enables also to solve the associated state estimation (filtering) problem. Additionally, statistical processing is performed for the obtained residuals, that is for the differences between the state vector of the monitored power system and the state vector provided by the aforementioned filter when the latter makes use of a fault-free model. It is shown, that the suitably weighted square of the residuals' vector follows the χ2 statistical distribution. This property allows to use confidence intervals and to define thresholds that demonstrate whether the distributed power system functions as its fault-free model or whether parametric changes have taken place in it and thus a fault indication should be given. It is also shown that the proposed statistical criterion enables fault isolation to be performed, that is to find out the specific power generators within the distributed power system which have exhibited a failure. The efficiency of the proposed filtering method for condition monitoring in distributed power systems is confirmed through simulation experiments