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Inspection of critical social infrastructures, which are mainly made of concrete, is a pressing issue. Weakly supervised methods are interesting for such critical tasks because they allow a unique mix of human involvement and automation. However, humans can make mistakes, resulting in the system being misled. In the present paper is proposed a framework for weakly supervised defect detection in concrete structures involving a consensus between several humans providing weak supervision. This allows to compensate for the shortcomings of each individual human and, therefore, yield better performance along with robustness to erroneous weak supervision. Experiments conducted with concrete test blocks in laboratory conditions showed the effectiveness of our proposed method.