Deformation analysis with kinematic deformation model

Deformacijska analiza je postopek ugotavljanja stabilnosti točk, kar je pri določanju premikov temeljnega pomena. Dobljene vrednosti premikov in deformacij predstavimo z deformacijskim modelom, le-ta pa opisuje najverjetnejši potek deformacije. V preteklosti so klasični postopki obravnavanja deformacij temeljili na kongruenčnem modelu. Z razvojem računalništva, merskih tehnik in algoritmov vrednotenja, pa se je spremenila tudi metoda deformacijske analize, ki poleg osnovne določitve geometrije objekta, vključuje še časovni potek premikov, lahko pa tudi vzroke za njihov nastanek. Osredotočili smo se na kinematični deformacijski model, pri katerem predpostavimo, da je obravnavani objekt nenehno v gibanju. S tem v model vpeljemo tudi časovno komponento. Na začetku dela smo postavili hipotezo, da uporaba kinematičnega deformacijskega modela pri kontrolnih meritvah geotehničnih objektov omogoča obravnavanje geometričnih sprememb objekta s časovnimi funkcijami. Na izbranem objektu, kjer je bilo že opravljenih več terminskih izmer, smo preverili stabilnost referenčnih točk in določili statistično značilne premike kontrolnih točk oziroma določili stabilnost le-teh s kongruenčnim deformacijskim modelom. Obravnavali smo časovni okvir, znotraj katerega so bili na določenih točkah že v preteklosti zaznani konkretnejši premiki. Kinematični deformacijski model izhaja iz skupne izravnave meritev v vseh terminskih izmerah, kjer sta poleg koordinatnih neznank, neznanki še hitrost in pospešek premika. Ker je tak sistem zahteven za izračun, smo izbrali tehniko filtriranja, točneje Kalmanov filter, ki omogoča oceno neznanih količin, v katerih je prisoten šum, kot funkcijo časa in pogrešenih meritev. Gre za algoritem, ki se pogosto uporablja v geodetskem inženirstvu, kjer ni mogoče zagotoviti nadštevilnih meritev. Temelji na določitvi stanja sistema po metodi najmanjših kvadratov, hkrati pa oceni tudi stopnjo zanesljivosti. V sklopu magistrskega dela smo izdelali program za obdelavo kinematičnih meritev s Kalmanovim filtrom za primer diskretnega kinematičnega modela. Testirali smo stabilnost kontrolnih točk ter rezultate prikazali numerično in grafično. Pričakovano je uporabljen pristop ponudil nekatere dodatne informacije (hitrost in pospešek premikov) o stanju obravnavanega objekta v prostoru in času, kar predstavlja alternativni pristop dosedanjemu kongruenčnemu modelu vrednotenja v deformacijski analizi.Deformation analysis is a procedure used for detecting the height of point stability, which plays the main role in determining displacements. The obtained displacement and deformation values are represented by using a deformation model, which describes the most probable deformation course. In the past classic procedures of deformation analysis were based on congruent model. Due to computing, measuring techniques and evaluation algorithm development also the deformation analysis method has changed. Besides basic determination of the object’s geometry it now also includes displacement timeline, as well as potentially the causes for their formation. We focused on kinematic deformation model in which we assumed that the given subject is constantly moving. Using that, we are also able to incorporate time component in the model. At the beginning of the thesis, we set a hypothesis that the use of kinematic deformation model in control measurements of geotechnical objects allows the geometric changes to be considered in connection with time functions. On the chosen object, where several epochs were made, we checked the reference point stability and determined the statistical significance displacements of control points or their stability with the help of congruent deformation model. We were considering the time frame in which severe movements at some points had already been detected before. Kinematic deformation model is based on adjustment of all the observations in all epochs where besides unknown coordinates also speed and acceleration displacements are unknown. Since this kind of system is hard to calculate, we chose a Kalman filter technique, which allows the evaluation of the unknown quantities. These unknown quantities may have some noise, such as time and miscalculated observation function. This kind of algorithm is commonly used in geodetic engineering, where it is not possible to ensure redundant measurements. It is based on the determination of the system condition using the least squares method, but at the same time it also evaluates the reliability degree. As part of the master’s thesis we made a programme for processing kinematic measurements by using the Kalman filter for the case of discreet kinematic model. We tested the stability of control points and displayed the results numerically and graphically. As expected, the used approach offered some additional information (speed and acceleration of the displacements) about the present object’s condition in space and time, which represents an alternative approach to the congruent evaluation model used in deformation analysis so far