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BASIS OF PRESENTATION - Impact Change on the Segment Income Previously Presented (Details) - USD ($)
 3 Months Ended 9 Months Ended
Sep. 30, 2023
Oct. 01, 2022
Sep. 30, 2023
Oct. 01, 2022
Assets acquired:        
Consolidated operating income $ 57,700,000 $ 37,300,000 $ 158,800,000 $ 75,900,000
Acquisition-related and other costs 2,900,000   5,000,000.0  
Amortization of intangible assets 14,600,000 6,700,000 32,400,000 23,100,000
Special charges, net 0 0 0 100,000
ITL        
Assets acquired:        
Acquisition-related and other costs   100,000   1,100,000
As Previously Presented        
Assets acquired:        
Consolidated operating income   37,300,000   75,900,000
Effect of Change        
Assets acquired:        
Consolidated operating income   0   0
Operating Segments        
Assets acquired:        
Consolidated operating income 91,600,000 63,400,000 250,400,000 159,100,000
Operating Segments | HVAC reportable segment        
Assets acquired:        
Consolidated operating income 58,300,000 33,100,000 161,200,000 82,000,000.0
Special charges, net   0   100,000
Operating Segments | Detection and Measurement reportable segment        
Assets acquired:        
Consolidated operating income 33,300,000 30,300,000 89,200,000 77,100,000
Special charges, net   0   0
Operating Segments | As Previously Presented        
Assets acquired:        
Consolidated operating income   56,600,000   134,900,000
Operating Segments | As Previously Presented | HVAC reportable segment        
Assets acquired:        
Consolidated operating income   30,900,000   71,700,000
Operating Segments | As Previously Presented | Detection and Measurement reportable segment        
Assets acquired:        
Consolidated operating income   25,700,000   63,200,000
Operating Segments | Effect of Change        
Assets acquired:        
Consolidated operating income   6,800,000   24,200,000
Operating Segments | Effect of Change | HVAC reportable segment        
Assets acquired:        
Consolidated operating income   2,200,000   10,300,000
Operating Segments | Effect of Change | Detection and Measurement reportable segment        
Assets acquired:        
Consolidated operating income   4,600,000   13,900,000
Corporate expense        
Assets acquired:        
Corporate expense 13,000,000.0 17,200,000 44,200,000 50,200,000
Corporate expense | As Previously Presented        
Assets acquired:        
Corporate expense   17,200,000   50,200,000
Corporate expense | Effect of Change        
Assets acquired:        
Corporate expense   0   0
Segment Reconciling Items        
Assets acquired:        
Acquisition-related and other costs 2,900,000 100,000 5,000,000.0 1,100,000
Long-term incentive compensation expense 3,400,000 2,100,000 10,000,000.0 7,700,000
Amortization of intangible assets 14,600,000 6,700,000 32,400,000 23,100,000
Special charges, net $ 0 0 $ 0 100,000
Other operating expense, net   0   1,000,000.0
Segment Reconciling Items | As Previously Presented        
Assets acquired:        
Acquisition-related and other costs   0   0
Long-term incentive compensation expense   2,100,000   7,700,000
Amortization of intangible assets   0   0
Special charges, net   0   100,000
Other operating expense, net   0   1,000,000.0
Segment Reconciling Items | Effect of Change        
Assets acquired:        
Acquisition-related and other costs   100,000   1,100,000
Long-term incentive compensation expense   0   0
Amortization of intangible assets   6,700,000   23,100,000
Special charges, net   0   0
Other operating expense, net   $ 0   $ 0