This functionality can be important while considering the hardware equipment for a planned monitoring system. There might also be constellations where environmental conditions that af­ fect data transmission—like meteorological parameters—should take part in the systematic variation. Analogous to hardware configurations, such constellations can also be modelled and handled as named composite subsets. The guiding idea of the structure described above is to automatically generate the list of all possible configurational variants instead of having to update such a list manually with every added or removed parameter option.

Although the experiment in general does not indicate unambiguous advan­ tages for particular variants of aggregation , it certainly reveals some preferences that should be considered in forthcoming experiments. Hardware The properties of the hardware involved in monitoring are listed in the next group of Table 5.1. Leaving factors like workload or algorithm unchanged, the energy demand is affected by the efficiency of sensors, communication devices and pro­ cessing units.

For the fields generated here, they are characterized by a normal distribution, the preset mean value µ and the standard deviation σ . In order to create normally distributed variables from uniformly distributed pseudo-random numbers, the well-known Box-Muller algorithm is used. When planning a monitoring system, the first task is to define the extent and to estimate the dynamism of the phe­ nomenon to be observed.

A mean value in the context of geostatistics should not be confused with the best available estimation of the “true value” as known from other disciplines, where, say, a physical constant is to be determined by multiple observations. For a regionalized variable there is no “true value” since its actual manifestation as a surface spreads over a whole range where values are autocorrelated according to their distance. The statistical properties of such a regionalized variable https://globalcloudteam.com/ are therefore more complex and have to take into account the correlation of observations. Depending on the applied covariance function, the filter grid has different extensions. If, for example, a spherical covariance function (see Figure 3.4, p. 43) is used for filter definition, the correlation between observations further apart than range is always zero. Therefore, the grid size of the filter does not need to extend more than corresponding distance for that dimension.

Where dji is the distance of the aggregated point j to the origin regarding dimension i and max is the maximum distance that occurs in the whole set of aggregated points. The value for each dimension and therefore also the product, is guaranteed to be between 0 and 1. Con­ sequently, only one step or level is needed to express one bit of information (last column in Listing 7.3, Section 7.4). 5.4.1 Problem Context The specific features introduced in the next two sections can best be explained in the context of a monitoring system architecture as sketched in Figure 5.13.

Conformal Invariance And Critical Phenomena, Hardcover By Henkel, Malte, Bran

These log files record all events that occur within the application, including the identification of security threats and the monitoring of critical operational indicators. As the IT organization coordinates the appropriate security measures to protect critical information assets, it can begin configuring a continuous monitoring software solution to collect data from those security control applications. Continuous monitoring, also known as ConMon or Continuous Control Monitoring , gives security and operations analysts real-time data on the entire health of IT infrastructure, including networks and cloud-based applications.

The undisputable high computational burden (O for the inversion of the covariance matrix) of kriging may disqualify the method where high throughput goes along with real-time requirements. In such cases, inverse distance weighting might be preferable due to its lower complexity . For operating an environmental monitor­ ing system it provides sophisticated means to address many problems that occur in this context.

Continuous Monitoring

The focus is on the representation of the continuous field as a whole, not on the time series of indi­ vidual sensors. With this in mind, it appears reasonable to filter out observations that do not significantly contribute to the description of the field before long-term archiving of the data. When embedded into a monitoring system, the approach would perform best after some deliberate depletion based on spatio-temporal statistics (see Section 5.4.1 and ). Progressive decompression can support different requirement profiles and is thus another important design feature of the approach.

The throughput per time unit depends on hardware specifications and communication bandwidth while the effort for transmission according to time and energy depends on the efficiency and bandwidth of the communication devices. The statistical properties described above can be used to determine the next dimension. So it might be reasonable to select the dimension with the greater extent or deviation for the next split.

Monitoring Continuous Phenomena : Background, Methods And Solutions, Hardcove

At this stage, we ignore temporal dynamism in order to exclude it as a fac­ tor for differences between the reference model and the sequential ap­ proach. Random observations are scattered over the model area, each assigned the value picked from the reference model at its position. Given this simulated measure­ ment set, a new model can be calculated by kriging (Figure 7.11). The derived model (Figure 7.11) differs from the reference model (Fig­ ure 7.11) due to interpolation uncertainty, but approximates it well when the number and distribution of samples are sufficient (see Section 5.3.2). Following the sequential strategy, subsets of the synthetic measurements are created and calculated sequentially in sub-models (see Figures 5.15 and 5.16 in Section 5.4.2). For the first subset (Figure 7.12), the deviations to the reference model are rather large and can be seen in the difference map .

In a simulated chemical disaster scenario, mobile geosensors are placed in a way that optimises the prediction of the pollutant distribution. Instead of optimising the observation procedure itself, we exploit the kriging variance in order to achieve efficient continuous model generation from massive and inho­ mogeneous data. Katzfuss & Cressie decompose a spatial process into a large-scale trend and a small-scale variation to cope with about a million observations. This so­ lution is an option for optimizing very large models, but is not helpful for our sequential approach with its real-time specific demands. Osborne et al. introduce a complex model of a gaussian process (syn­ onym for kriging) that incorporates many factors like periodicity, measurement noise, delays and even sensor failures.

This alleviates situations where the Gauss-Newton algo­ rithm does not converge or finds several local minima. Interpolation by kriging Given the parameters as derived from the vari­ ogram fitting, the interpolation can be performed at arbitrary positions and therefore also for arbitrary grid resolutions to fill spaces between observa­ tions. Beside the value itself, kriging also provides the estimation variance derived from its position relative to the observa­ tions it is interpolated from [89, p. 464], . The computational effort for kriging can be reduced when subsets of observations are processed and merged sequen­ tially. Merging can also be used to seamlessly integrate new observations into existing models. Higher level queries Statements about continuous phenomena like an ex­ ceeded threshold of pollutants of a particular region within a particular period of time can not easily be drawn from raw sensor data.

• This effect is less obvious in Figure 7.6, which represents sampling epochs performed on a three-dimensional random field.
• Organizations are unable to recognize, resolve, or comprehend critical insights on specific hazards due to a lack of continuous monitoring.
• Given ade­ quate knowledge about these two conditions, the monitoring system should be designed to sufficiently mediate between them [13, p. 6].
• So the concept of a virtual sensor as introduced in Chapter 6 might serve as a useful and generic concept in this context.
• This effect is comprehensible since sparse sampling will generate surfaces that are smoother than the actual phenomenon.
• The differing characteristics of correla­ tion decay in space and time and also spatio-temporal interdependencies can thus be inspected.

For some applications, it might be reasonable to give response time behaviour (at least for first coarse results) a higher priority than full accuracy after performing one step of trans­ mission. The parameters above do not take into account the specific structure of geo­ statistical parameters. They assume the observations to be independent and iden­ tically distributed , which is not the case since they are spatio­ temporally correlated. In reality, they rather represent a regionalized variable with a constant mean or trend, a random but spatio-temporally correlated com­ ponent and an uncorrelated random noise [19, p. 172], [21, p. 11].

Disjunctive Kriging Disjunctive kriging transforms the primary variable to polynomials that are kriged separately and summed afterwards. It is applied when the primary variable does not sufficiently represent a normal distribution. This decrease is ex­ pressed as the inverse of the distance Continuous monitoring development background with an exponent bigger than zero. She’s devoted to assisting customers in getting the most out of application performance monitoring tools. Loupe – One of the most useful functions is the automatic grouping of your log events, which saves you time while looking for the root of an issue.

More complex definitions where several parameters and conditions are combined might also be reasonable to adapt to such data structures, but they are not regarded here. Coverage When a region is to be monitored, not only its extent, but also the observational density has to be considered for both space and time. Monitoring continuous phenomena by stationary and mobile sensors has become a common due to the improvement in hardware and communication infrastructure and decrease in it’s cost. Sensor data is now available in near real time via web interfaces and in machine-readable form, facilitated by paradigms like the Internet of Things . When combining the variations within a process chain, the number of possible config­ urations to test and evaluate might quickly multiply to large numbers.

Monitoring Continuous Phenomena: Background, Methods And Solutions

Assuming this merging procedure, spatially isolated or temporally outdated observations can keep their influence over multiple merging steps, depending on the decay function (Equation 5.19). This is especially helpful when no better observations are available to overwrite them. Nevertheless, by using the kriging variance, the growing uncertainty of such an estimation can be expressed, which can then be considered where it appears relevant for monitoring and analysis. Apart from some loss of accuracy, the strategy of sequencing comes along with several advantages. This can be carried out while, in principle, the advantages of kriging like the unbiased and smooth interpolation of minimum variance and the estimation of uncertainty at each position, are retained. In many cases, the dynamism of the continuous field is only roughly known in advance and is therefore not revealed until the data is processed.

Therefore, the algorithm keeps track of the statistical properties of each dimension separately. So for each set of points the minimum, maximum, extent, mean, median and variance are calculated per di­ mension and can thus be used as control parameters for the points of decision that are described below. Depending on the size of the filter grid and the current filter position, there is a considerable amount of filter cells that lie outside the target grid. Consequently, they do not contribute to the average value assigned to the target cell on which the filter centre is currently positioned. The proportion of outside filter cells increases towards the fringes and even more towards the corners of the target grid, also depending on the dimensionality.

Variogram Fitting

In the course of my work he was both critical and inspiring and thus often enough paved the way for significant progress. As my first doctoral supervisor, Manfred Ehlers provided some very valuable hints to significantly improve the quality of my dissertation and therefore of this book too. Especially in the final phase of the book project, I drew much benefit from discussions about pursuing ideas with Folkmar Bethmann. His open-mindedness towards complex problems was inspiring to me and helped to advance these approaches.

Beside the deviation from the reference model, also the actual computational effort that is necessary for each variant can be considered. This makes it possible to quantify and thus compare the efficiency of different approaches. By abstracting the computational effort of a particular calculation from the hardware, it is used in principle possible to estimate the expenses incurred in terms of time and energy for any other given computer plat­ form. This can be a critical aspect for wireless sensor networks, large models and environments with real time requirements.

Continuous Intelligence

In many cases it is appropriate to relate this value to the one of the total set that the procedure started with to get a relative value. For a uniform splitting pattern, the algorithm can also simply toggle between all dimensions without any parameter checking. Within this solution, consecutive splits by the same dimension are allowed, which might be useful for very anisotropic point distributions.

The principle that is applied for the compression method is derived from the Bi­ nary Space Partitioning tree (BSP tree, ). Unlike its common utilization for indexing, it is used here as a compression method that is applied to each single observation in a dataset. Consequently, the algorithm does not need to keep track of individual sensors within a set of ob­ servations, but encodes each observation individually within the value domains given per variable dimension. The general idea behind the design is to encode observations describing a continuous phenomenon within a (spatio-temporal) region.