yingdea, I can see many issues with your design that make the output sensitive to input level.
The LM358 has no operation within 1.5 to 2V near each supply rail and your design, Vee=ground.
Thus any signal less than 2V above ground is distorted (in your case dead band with inversion).
Fix. Use a split supply, virtual mid V+ reference or a "rail to rail" Op Amp type. :smile:
The second design is no better as a buffer , with a 200 source impedances you can do same as this with a 2V rectifier diode an no op-amp. :-o
If you must use a single supply say so. 8-O
If you must sense low currents, specify the min input V level which is designed by input offset error. :shock:
Assuming this is not AC Line and Neutral , beware of Neutral to ground offset from ground faults and long wires which may coupline stray noise without a filter.
Fix .. Add an EMI filter (small cap ) on Feedback of Op Amp
LPF set at or above max freq..