TAI, International Atomic Time, ticks according to the second defined by the International System of Units. TT, Terrestrial Time, is separated from TAI by 32.184 seconds.
The second was once defined by the rotation of the Earth, with 86400 seconds per mean solar day. This concept is the basis for UT1, Universal Time. Atomic Time and Universal Time are rather distinct time scales. The Earth's rotation rate is ever so slowly slowing down.This means that a UT1 second is not equal to a TAI second.
Coordinated Universal Time, UTC, is a hybrid time scale. It has seconds that tick in sync with Atomic Time but also has leap seconds introduced intermittently so as to keep UTC and UT1 within 0.9 seconds of one another.
In my opinion, all the key point maybe the TAI. We can derive the TAI-UT1 by astronomical observation and then compute other time scales with the relationship formula. Am I right?
No, you're not. The very slow slowing down of the Earth's rotation rate due to transfer of angular momentum to the Moon is compounded with changes that occur over multiple time scales, varying from centuries to days long (or even shorter; earthquakes are hypothesized to change the Earth's inertia tensor and hence the rotation rate). Some of these changes are predictable, to some extent; others are not predictable at all.
The unpredictability means that $\Delta T \equiv TT - UT1$ is not predictable. This is why the primary job of a number of observational scientists is to collect data regarding the observed Earth rotation rate and publish it via various means. You can receive these data from the International Earth Rotation and Reference System Service (IERS) via its Bulletins A and B. You can also subscribe to these bulletins via email.
Side note regarding the acronyms:
TAI obviously does not jibe with International Atomic Time. (It does jibe in French.) A time scale that I didn't mention, GMST (Greenwich Mean Sidereal Time), does jibe with its acronym, in English. UTC doesn't jibe with Coordinated Universal Time in any language. The acronyms for these internationally recognized time scales are the same in every language.
IERS also obviously does not jibe with International Earth Rotation and Reference System Service. It did do so, once upon a time (in English), when the organization's name was shorter. The acronym remains IERS, in every language.