{"id":3088,"date":"2024-09-13T16:18:58","date_gmt":"2024-09-13T14:18:58","guid":{"rendered":"https:\/\/test.kint.cz\/?p=3088"},"modified":"2025-06-04T19:32:41","modified_gmt":"2025-06-04T17:32:41","slug":"4-2-data-processing-and-analysis","status":"publish","type":"post","link":"https:\/\/test.kint.cz\/en\/4-2-data-processing-and-analysis\/","title":{"rendered":"4.2 Data processing and analysis"},"content":{"rendered":"\t\t
\n\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t

4.2 Data processing and analysis<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t

For deriving dependencies in complex critical infrastructure, in the case of use, i.e., metro infrastructure, the sensitivity theory is applied in the presented work, which allows the strength of individual dependencies to be evaluated, i.e., their vulnerability, meaning the ability of dependencies to cause failure (KI, metro). The matrices are transformed into a graph for subsequent analysis.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

\n\t\t\t\t
\n\t\t\t\t\t

4.2.1 Theory of sensitivity<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t

For better interpretation and working with information systems, vulnerability can also be defined as sensitivity using sensitivity theory [87,88], which can be queried with the following relation [89]<\/a>:<\/p>

\"Data<\/figure>

(22)<\/p>

where Si<\/em><\/strong> is the absolute sensitivity of the output function y to the parameter of the input function xi<\/sub><\/strong>. According to the source [90]<\/a>, in terms of electronic systems, y = f(x1,..,,xi,\u2026,xN)<\/strong> is the network (or system) function, which depends on the circuit parameter xi<\/sub><\/strong>. The change in the system’s output function is therefore dependent on its sensitivity and on the change in input parameters xi<\/sub><\/strong>, and the relation is for practical reasons expressed in matrix form, i.e., using the sensitivity matrix S<\/em><\/strong> <\/em><\/strong>[90]<\/a>:<\/p>

\"Data<\/figure>

(23)<\/p>

For electrical, electronic, and programmable electronic systems (hereinafter referred to as E\/E\/PE), it is advantageous to consider relative sensitivity and the relative change in parameters, as it allows for the calculation of output variable tolerances, the design of input parameter tolerances, optimization of circuit sensitivity, finding the most sensitive components, i.e., components with the greatest impact on changes in the output variable [90]<\/a>.<\/p>

For working with assets, it is suitable to work with absolute sensitivity, because although the scales for evaluating criticality are normalized, each asset function has a different physical basis.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

\n\t\t\t\t
\n\t\t\t\t\t

4.2.2 Matrix notation and codification of names<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t

It is customary in practice to present the relationships of individual elements in tables. In our case, it concerns sensitivity, i.e., the relationship of input variables (hazards, i.e., assets) and output variables (system functions, i.e., assets):<\/p>

For better clarity, a matrix notation is used, as shown in Table 8.<\/p>

Table<\/a> 8 Format of the asset criticality table for individual hazards.<\/p>

<\/td> Hazard 1<\/em><\/strong><\/td> … <\/em><\/strong><\/td> Hazard n<\/em><\/strong><\/td> <\/tr>
Asset 1<\/em><\/strong><\/td> S11<\/td> … <\/td> Sn1<\/td> <\/tr>
\u2026<\/em><\/strong><\/td> .<\/td> … <\/td> .<\/td> <\/tr>
Asset m<\/em><\/strong><\/td> S1m<\/td> … <\/td> Snm<\/td> <\/tr> <\/tbody> <\/table> <\/figure>

Table 8 is converted into matrix form, where yi<\/sub><\/em><\/strong> represents assets and xi<\/sub><\/em><\/strong> represents hazards. The matrix notation allows performing necessary operations and converting the matrix into a graph for scenario analysis.<\/p>

\"Data<\/figure>

(24)<\/p>

The input parameters xi<\/sub> <\/em><\/strong>can actually represent output parameters of other assets (functions). If we wish to display the relationships in greater depth, we can create a chain using both input and output parameters on both sides of the equation, i.e., for the purposes of this work, “chained sensitivity matrices,” which in engineering represent the degree of vulnerability dependent on the degree of interconnection of variables or parameters [6,33]<\/a>.<\/p>

In practice, these tables and matrices can become large, and to ensure their readability, it is advisable to introduce an appropriate coding of names. The dissertation uses numerical designations for hazards listed in Appendix B. The designation of asset groups used is given in Table 9.<\/p>

Table<\/a> 9 Designation of asset groups used.<\/p>

Group<\/em><\/strong><\/td> Designation<\/em><\/strong><\/td> <\/tr>
Construction<\/td> AK<\/td> <\/tr>
Technology<\/td> AT<\/td> <\/tr>
Personnel<\/td> AP<\/td> <\/tr>
Locations<\/td> AM<\/td> <\/tr>
Functions<\/td> AF<\/td> <\/tr>
Connections and flows<\/td> AV<\/td> <\/tr>
Organization and economy<\/td> AO<\/td> <\/tr> <\/tbody> <\/table> <\/figure>

The numerical designation of individual asset classes used below in the dissertation is due to their large scope provided in Appendix C.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

\n\t\t\t\t
\n\t\t\t\t\t

4.2.3 Transformation of matrices into a graph<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t

Using graph theory, as described, for example, in the work [91],<\/a> vulnerabilities can be displayed using a weighted directed graph. To create the graph, the following steps are required:<\/p>