Multi-way principal component analysis(MPCA)has received considerable attention and been widely used in process monitoring.A traditional MPCA algorithm unfolds multiple batches of historical data into a two-dimensional matrix and cut the matrix along the time axis to form subspaces.However,low efficiency of subspaces and difficult fault isolation are the common disadvantages for the principal component model.This paper presents a new subspace construction method based on kernel density estimation function that can effectively reduce the storage amount of the subspace information.The MPCA model and the knowledge base are built based on the new subspace.Then,fault detection and isolation with the squared prediction error(SPE)statistic and the Hotelling(T2)statistic are also realized in process monitoring.When a fault occurs,fault isolation based on the SPE statistic is achieved by residual contribution analysis of different variables.For fault isolation of subspace based on the T2 statistic,the relationship between the statistic indicator and state variables is constructed,and the constraint conditions are presented to check the validity of fault isolation.Then,to improve the robustness of fault isolation to unexpected disturbances,the statistic method is adopted to set the relation between single subspace and multiple subspaces to increase the corrective rate of fault isolation.Finally fault detection and isolation based on the improved MPCA is used to monitor the automatic shift control system(ASCS)to prove the correctness and effectiveness of the algorithm.The research proposes a new subspace construction method to reduce the required storage capacity and to prove the robustness of the principal component model,and sets the relationship between the state variables and fault detection indicators for fault isolation.
The twin-tube shock absorber was studied and the relevant factors of thermal equilibrium were simulated. The dynamic model of the shock absorber was constructed and simulation curves of force-displacement and force-velocity were output. The experiment of the twin-tube shock absorber was carried out,and the results were compared with the modeling resultss. Further,the vibration energy regeneration model was established,and the bench simulation study was carried out. The results showed that the energy regeneration model not only absorbed shock energy but also converted vibration energy into electricity energy.
