Results

Control commands are identified by numerically simulating the behavior of the structure using the dynamic relaxation method. They are then applied to the laboratory structure. Errors due to modeling and nonlinear behavior during the control command application lead to inaccuracies. For one applied point-load, the slope compensation varies between 79 and 100%, whereas for two point-loads the slope compensation varies between 65 and 100%. These second load cases are more difficult to compensate because of nonlinearity effects. If the compensation is not sufficient, it is possible to search a second control command using the first search final state as the second search initial state.

The case-based reasoning method makes it possible to create a structure that learns through using its own experience. Memorizing past altered configurations and the corresponding control command makes it possible to react faster to new applied loads by adapting past solutions. Control command search using case-based reasoning method is always faster then using stochastic search only. Moreover, the number of iterations needed to identify a control command decreases with increasing number of cases in the case-base, see the example in Figure 3. Improvements of up to 40 times have been observed. The structure does not learn regularly because of the stochastic nature of the process. Cases are retrieved from the case-base by comparing their notional “distance” to the actual task, considering altered slope value and active strut lengths.

Iterations

Figure 3: The structure learns as cases are added to the case-base (Domer and Smith, 2005)

The structure is perturbed by the control system to carry out self-diagnosis. This paper presents an initial numerical study. The goal of this study is to localize a broken lateral cable, knowing that the structure is not loaded. The initial example is that the broken cable is cable number 111. At the beginning, all thirty lateral cables in the five modules are present in the space of possible broken cables. The identification process assumes successively that each non rejected candidate has a broken lateral cable. The first micro-movement (strut 148: +1mm) makes it possible to eliminate twenty-two candidates since these situations involved behavior that was opposite in direction to that measured for cable 111. The second one (strut 60: +1mm) eliminates other four possible broken cables and then the third micro-movement (strut 60: -1mm and strut 148: +1mm) eliminates three more potentially broken cables and makes it possible to identify the broken lateral cable 111.

Micro-movements of active struts at the center of the structure eliminate candidates faster than micro-movements of active struts situated at the edge of the structure. Combining two micro­movements sometimes makes it possible to further eliminate candidates. It is not always possible to isolate one candidate with single micro-movements.

Once identified, this local damage can be compensated through applying a control command such that the structure still satisfies the serviceability criterion. Therefore the structure can still accept loads considering a loss of carrying capacity.

In this study point-loads are applied at nodes 37, 43 and 48. The maximum load in Newtons for which the structure can compensate the slope when the cable 111 is broken is presented at the second line of Table 1 (CC LD: Carrying Capacity with Local Damage). The maximum load for which the structure can compensate the slope when it is not damaged is shown at third line of Table 1 (CC NLD: Carrying Capacity with No Local Damage). The loss percentage of carrying capacity is indicated on the last line of Table 1. The loss of carrying capacity is understandably larger in the vicinity of the local damage (nodes 37 and 48 are close to cable 111). In these cases loads which should have passed through the broken element to reach the supports have to find another path.

Table 1. Loss of carrying capacity when the lateral cable 111 is broken

Node

37

43

48

CC LD [N]

350

440

310

CC NLD [N]

840

520

800

CC Loss %

58

15

61