Method for detecting a leakage during operation of a braking system for a vehicle and braking system for a vehicle

A braking system for a vehicle, comprising:

• an actuating circuit including a final control system actuatable with the aid of an actuating unit for generating a braking intention signal;
• an active circuit having a pressure generation unit that includes a displacement piston movable in a translatory manner;
• at least one wheel brake coupled hydraulically to the pressure generation unit;
• a sensor unit for detecting an actual braking pressure in the active circuit;
• and
• a control unit that is connected to the final control system of the actuating circuit, to the sensor unit, and to the pressure generation unit of the active circuit, wherein:
• the control unit ascertains, from the braking intention signal, a setpoint braking pressure required in the active circuit,
• the control unit activates the pressure generation unit for setting the actual braking pressure in the active circuit by moving the displacement piston according to the setpoint braking pressure;
• the control unit activates the pressure generation unit for carrying out a pressure modulation, including setting the actual braking pressure in the active circuit to a value greater than the setpoint braking pressure and lowering the actual braking pressure until the setpoint braking pressure is reached, by moving the displacement piston at a predetermined piston speed,
• the control unit ascertains, from the actual braking pressure detected with the aid of the sensor unit, a chronological pressure gradient, as the actual braking pressure is being lowered, during the pressure modulation, and
• the control unit detects a leakage of the active circuit based on the detected pressure gradient when the pressure gradient is outside a range predetermined for the piston speed.