All, posted in this discussion:
where I replied once, but now I have found the same basic question in this new discussion, I will only answer here.
I haven't seen the model of the structure that has the bolts in it, but I would not go directly to a nonlinear transient structural simulation. Is it known that the bolt was not broken after the sine sweep?
Let's assume the bolt broke during the Random Vibration test. What was the duration of the Random Vibration? How was the duration determined? How was the PSD profile determined?
Is it known that the bolt was correctly torqued before the test began? What else besides torque was applied to prevent bolt loosening? For example, a thread lock adhesive, other mechanical device. Were the other bolts checked for loss of preload?
Let's assume that the bolt was correctly installed into the structure according to the specified torque and that there was a thread lock device/adhesive. Let's also assume that the Random Vibe profile and duration are appropriate, therefore the issue is the bolted joint design.
To design a bolted joint, you need to extract the forces and moments that go through that bolt during the Random Vibration profile. Since Random Vibe is a statistical result, you need to take 5 sigma values to design with.
Once you have the forces and moments, check that the bolt size selected and the preload created with the appropriate torque for that size will support the maximum expected forces. Specifically, that the normal forces do not allow the joint to open and the shear forces do not allow the joint to slip. For this you need to know the coefficient of friction between the faces that are being bolted together.