Temporal redundancy

Typically, process data are improved using spatial, or functional, redundancies in the process model. Measurements are spatially redundant if more than enough data exist to completely define the process model at any instant, that is, the system is overdetermined and requires a solution by least squares fitting. Similarly, data improvement can be performed using temporal redundancies. Measurements are temporally redundant if past measurement values are available and can be used for estimation purposes. Dynamic models composed of algebraic and differential equations provide both spatial and temporal redundancy. 

Under dynamic or quasi-steady-state conditions, a continuously monitored process will reveal changes in the operating conditions. When the process is sampled regularly, at discrete periods of time, then along with the spatial redundancy previously defined, we will have temporal redundancy. If the estimation methods presented in the previous chapters were used, the estimates of the desired process variables calculated for two different times, t and t2, are obtained independently, that is, no previous information is used in the generation of estimates for other times. In other words, temporal redundancy is ignored and past information is discarded. 

In this chapter, the data reconciliation problem for dynamically evolving processes is considered. Thus, temporal redundancy is taken into account by using... 

In addition, conventional approaches assume that the only available information about the process is the known model constraints. However, a wealth of information is available in the operating history of the plant. In this case, together with spatial redundancy, there is also temporal redundancy, that is, temporal redundancy exists when measurements at different past times are available. This temporal redundancy contains information about the measurement behavior such as the probability distribution. The methods discussed in the first two sections of this chapter try to exploit these ideas by formulating the reconciliation problem in a different way. 

Virtually aU applications of video and visual communication deal with enormous amount of data. Because of the volume of data, compression is an integral part of aU video applications. A compression system reduces the volume of data by exploiting spatial and temporal redundancies and by eliminating the data, which cannot be displayed suitably by the associated display or imaging devices. Its main objective is to retain as little data as possible, but sufficient to reproduce the original images without causing much distortion. 

Motion estimation is a process to determine the motion vector in a video sequences by reducing temporal redundancy between consecutive successful video frames [1, 2], Motion estimation identifies blocks that match each other in a video sequences by detecting objects transformation which appears in each frames but at different locations [3], The identified blocks will be represented with a motion vector (x, y) to indicate the motion pixel displacement in frames [4], Differences of values in pixels indicate that there are changes occurred in the frames. Block Matching Algorithm (BMA) technique is widely used for motion estimation where a frame is divided into square size of macro blocks [5, 6], The pixels values of the macro blocks which are divided will be used to compare between current macro block with the subsequent macro block [7, 8, 9] in the same frame. 

Program executed once per cycle Temporal redundancy of the execution of the safety program... 

Chen, J., and Romagnoli, J. A. (1997). Data reconciliation via temporal and spatial redundancies. IFAC-ADCHEM, pp. 647-653. 

Regulation of anthocyanin production involves transcriptional activators of the R2R3 MYB and the basic helix-loop-helix (bHLH) (or MYC) types (Table 3.2). This was first revealed by studies of the monocot Z. mays. It was found that the anthocyanin pathway is turned on in this species through the combined action of one member of the COLORED ALEURONEl (C1)/PURPLE PLANT (PL) MYB family and one member of the REDl (R)/BOOSTERl (B) bHLH family. The members of the MYB and bHLH families are functionally redundant, and their specific expression patterns enable spatial and temporal control of anthocyanin biosynthesis. 

The apparent contradiction between inflammatory chemokine and chemokine receptor redundancy observed in vitro and specific phenotypes revealed from gene-targeted animals can be resolved if one considers that these chemokines and their receptors function as a cooperative network in vivo to generate a complete immune response. Cooperation exists by coordinating the temporal expression of chemokine receptors on different cell types, the same cell type, or even the same cell. 

On the other hand, when more than one fault can influence the system at the same time, advanced diagnostic methods are used. These methods are based on parameter estimation. Sensitivity bond graph formulation [12] allows real-time parameter estimation and thus it is possible not only to isolate multiple faults but also to quantify the fault severities. Parameter estimation in single fault [2] or multiple fault scenarios [12] are essential steps to be performed before fault accommodation. The parameter estimation scheme also gives the temporal evolution of system parameters. Thus, it is possible to identify and quantify different kinds of fault occurrences. A progressive fault shows gradual drift in estimated parameter values and intermittent fault shows spikes in the estimated parameter values. The advances made in the field of control theory have made it possible to develop state and parameter estimators for various classes of nonlinear systems. Analytical redundancy relations may also be used in optimization loop for parameter estimation because it avoids the need for state estimation. Interested readers may see Ref. [3] for further details and some solved examples. 

Redundancies (1) Spatial—correlation within a still image or a video frame data, (2) spectral—correlation between different color components of image elements, (3) temporal—correlation between successive frames of a video file. 

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