Andy, who moved from the Ospreys to the Warriors in the summer on a two-year contract, has already suffered two defeats against Welsh opposition in the Magners League this season.
Glasgow threw away a 20-0 advantage against the Dragons on the opening weekend of the season with Ceri Sweeney kicking a last-minute match-winning penalty.
This was followed a week later by a convincing defeat the hands of the Scarlets at Stradey Park.
"We have played two Welsh regions so far this season and I have ended up on the losing side both times," said Andy in the South Wales Echo.
"We are still kicking ourselves after losing to the Dragons after being 20 points up. We played well against the Scarlets but they produced some wonderful rugby and are going to be a strong side this season."
But while hoping it is a case of third time lucky, Andy does not expect the Blues to provide a lesser challenge than their Welsh rivals.
"I think I have only won at Cardiff once with the Ospreys and it is such a tough place to go and play," said Andy. "On their day, the Blues could be world beaters and we have to be careful because they will be hurting from two defeats."
But Glasgow will go into the Celtic clash with renewed confidence having beaten Heineken Cup champions Munster at Hughenden last weekend.
This was the Warriors first victory out of three matches this season, an identical record to the Blues whose only victory has also come at home to Munster.
"The victory against Munster has really boosted us and we are looking to kick on against Cardiff Blues," said Andy.
"Not many people in Wales know a lot about the Scottish players. But before I signed and since I have been here I have seen that Glasgow are a good side who like to play an exciting brand of rugby."
The 28-year-old, one of only eight Welshmen to have won the Heineken Cup following his success with Northampton in 2000, made the transition to Scotland in the summer after four seasons in Wales with Neath and the Ospreys.
Faced with competition with the likes of Wales locks Brent Cockbain, Ian Evans and Alun Wyn Jones, the 6ft 19st lock sought a new challenge.
"I needed a change, a new perspective if you like after being in the pressure cooker of Welsh rugby for the last four years," said the former Wales A and Under-21 second-row.
"It is completely different up here from in Wales. The city is geared so much towards football that there is not much attention given to rugby players which can be a blessing at times."