A recursive Kernel eigenspace updating algorithm was proposed to build the soft sensor for end-product quality.The updating procedure was composed of two sub-stages

i.e.firstly performing forward increasing updating and then followed by backward decreasing updating

which drastically decreased the required computation workload.Further

the whole Kernel matrix did not need to be stored.Simulation study on the Tennessee Eastman process showed that the consequent impurity component model had satisfying precision under both normal and faulty operations

which was obviously superior to the offline batch model and meanwhile approximated the performance of model obtained by successively applying the time-consuming traditional eigenvalue numerical algorithm.