REVENUES FROM CONTRACTS - Disaggregated Revenue (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Oct. 01, 2022	Oct. 02, 2021	Oct. 01, 2022	Oct. 02, 2021
Disaggregation of Revenue [Line Items]
Revenues	$ 370.5	$ 285.7	$ 1,031.6	$ 869.5
Revenues recognized at a point in time
Disaggregation of Revenue [Line Items]
Revenues	329.3	248.6	919.3	767.3
Revenues recognized over time
Disaggregation of Revenue [Line Items]
Revenues	41.2	37.1	112.3	102.2
Package and process cooling equipment and services, and engineered air quality solutions
Disaggregation of Revenue [Line Items]
Revenues	134.5	104.1	381.8	317.3
Boilers, comfort heating, and ventilation
Disaggregation of Revenue [Line Items]
Revenues	93.3	75.2	257.8	223.0
Underground locators, inspection and rehabilitation equipment, and robotic systems
Disaggregation of Revenue [Line Items]
Revenues	61.5	60.1	194.1	193.4
Communication technologies, obstruction lighting, and bus fare collection systems
Disaggregation of Revenue [Line Items]
Revenues	81.2	46.3	197.9	135.8
HVAC
Disaggregation of Revenue [Line Items]
Revenues	227.8	179.3	639.6	540.3
HVAC | Revenues recognized at a point in time
Disaggregation of Revenue [Line Items]
Revenues	212.2	154.1	588.1	474.8
HVAC | Revenues recognized over time
Disaggregation of Revenue [Line Items]
Revenues	15.6	25.2	51.5	65.5
HVAC | Package and process cooling equipment and services, and engineered air quality solutions
Disaggregation of Revenue [Line Items]
Revenues	134.5	104.1	381.8	317.3
HVAC | Boilers, comfort heating, and ventilation
Disaggregation of Revenue [Line Items]
Revenues	93.3	75.2	257.8	223.0
HVAC | Underground locators, inspection and rehabilitation equipment, and robotic systems
Disaggregation of Revenue [Line Items]
Revenues	0.0	0.0	0.0	0.0
HVAC | Communication technologies, obstruction lighting, and bus fare collection systems
Disaggregation of Revenue [Line Items]
Revenues	0.0	0.0	0.0	0.0
Detection and Measurement
Disaggregation of Revenue [Line Items]
Revenues	142.7	106.4	392.0	329.2
Detection and Measurement | Revenues recognized at a point in time
Disaggregation of Revenue [Line Items]
Revenues	117.1	94.5	331.2	292.5
Detection and Measurement | Revenues recognized over time
Disaggregation of Revenue [Line Items]
Revenues	25.6	11.9	60.8	36.7
Detection and Measurement | Package and process cooling equipment and services, and engineered air quality solutions
Disaggregation of Revenue [Line Items]
Revenues	0.0	0.0	0.0	0.0
Detection and Measurement | Boilers, comfort heating, and ventilation
Disaggregation of Revenue [Line Items]
Revenues	0.0	0.0	0.0	0.0
Detection and Measurement | Underground locators, inspection and rehabilitation equipment, and robotic systems
Disaggregation of Revenue [Line Items]
Revenues	61.5	60.1	194.1	193.4
Detection and Measurement | Communication technologies, obstruction lighting, and bus fare collection systems
Disaggregation of Revenue [Line Items]
Revenues	$ 81.2	$ 46.3	$ 197.9	$ 135.8