Dissertation topic in one field and degree in another field?
You write that you do not feel confident in your knowledge. However, experts in your field have put your knowledge to the test, and deemed it worthy of publication in a journal. Not once, not twice, but three times. Trust those experts. If they think your knowledge is good enough for three journal publications, then the committee members are highly likely to think similarly positively about your dissertation.

A solid background in mathematics is fertile ground for an exceptional career in any engineering discipline. If you stop worrying about the limitations of your knowledge, and instead accept that everyone's knowledge is by definition limited, you have a bright future ahead of you.