During construction,the shield linings of tunnels often face the problem of local or overall upward movement after leaving the shield tail in soft soil areas or during some large diameter shield projects.Differential ...During construction,the shield linings of tunnels often face the problem of local or overall upward movement after leaving the shield tail in soft soil areas or during some large diameter shield projects.Differential floating will increase the initial stress on the segments and bolts which is harmful to the service performance of the tunnel.In this study we used a random forest(RF)algorithm combined particle swarm optimization(PSO)and 5-fold cross-validation(5-fold CV)to predict the maximum upward displacement of tunnel linings induced by shield tunnel excavation.The mechanism and factors causing upward movement of the tunnel lining are comprehensively summarized.Twelve input variables were selected according to results from analysis of influencing factors.The prediction performance of two models,PSO-RF and RF(default)were compared.The Gini value was obtained to represent the relative importance of the influencing factors to the upward displacement of linings.The PSO-RF model successfully predicted the maximum upward displacement of the tunnel linings with a low error(mean absolute error(MAE)=4.04 mm,root mean square error(RMSE)=5.67 mm)and high correlation(R^(2)=0.915).The thrust and depth of the tunnel were the most important factors in the prediction model influencing the upward displacement of the tunnel linings.展开更多
For two r-graphs T and H,let ex_(r)(n,T,H)be the maximum number of copies of T in an n-vertex H r-graph.The determination of the Turán number ex_(r)(n,T,H)has become the fundamental core problem in extremal graph...For two r-graphs T and H,let ex_(r)(n,T,H)be the maximum number of copies of T in an n-vertex H r-graph.The determination of the Turán number ex_(r)(n,T,H)has become the fundamental core problem in extremal graph theory ever since the pioneering work of Turán’s theorem was published in 1941.Although we have some rich results for the simple graph case,only sporadic results have been known for the hypergraph Turán problems.In this paper,we mainly focus on the function ex_(r)(n,T,H)when H is one of two different hypergraph extensions of the complete bipartite graph K_(s,t).The first extension is the complete bipartite r-graph K^((r))_(s,t),which was introduced by Mubayi and Verstraëte(2004).Using the powerful random algebraic method,we show that if s is sufficiently larger than t,then ex_(r)(n,T,K^((r))_(s,t))=Ω(n^(v−e/t)),where T is an r-graph with v vertices and e edges.In particular,when T is an edge or some specified complete bipartite r-graph,we can determine their asymptotics.The second important extension is the complete r-partite r-graph K^((r))_(s1,s2,…,sr,)which has been widely studied.When r=3,we provide an explicit construction giving ex_(3)(n,K^((3))_(2,2,7))≥1/27n19/7+o(n19/7).Our construction is based on the norm graph,and improves the lower boundΩ(n73/27)obtained by the probabilistic method.展开更多
This letter gives a random construction for Low Density Parity Check (LDPC) codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has great flexible choice in LDPC...This letter gives a random construction for Low Density Parity Check (LDPC) codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has great flexible choice in LDPC code's parameters including codelength, code rate, the least girth of the graph, the weight of column and row in the parity check matrix. The method can be applied to the irregular LDPC codes and strict regular LDPC codes. Systemic codes have many applications in digital communication, so this letter proposes a construction of the generator matrix of systemic LDPC codes from the parity check matrix. Simulations show that the method performs well with iterative decoding.展开更多
基金supported by the Basic Science Center Program for Multiphase Evolution in Hyper Gravity of the National Natural Science Foundation of China(No.51988101)the National Natural Science Foundation of China(No.52178306)the Zhejiang Provincial Natural Science Foundation of China(No.LR19E080002).
文摘During construction,the shield linings of tunnels often face the problem of local or overall upward movement after leaving the shield tail in soft soil areas or during some large diameter shield projects.Differential floating will increase the initial stress on the segments and bolts which is harmful to the service performance of the tunnel.In this study we used a random forest(RF)algorithm combined particle swarm optimization(PSO)and 5-fold cross-validation(5-fold CV)to predict the maximum upward displacement of tunnel linings induced by shield tunnel excavation.The mechanism and factors causing upward movement of the tunnel lining are comprehensively summarized.Twelve input variables were selected according to results from analysis of influencing factors.The prediction performance of two models,PSO-RF and RF(default)were compared.The Gini value was obtained to represent the relative importance of the influencing factors to the upward displacement of linings.The PSO-RF model successfully predicted the maximum upward displacement of the tunnel linings with a low error(mean absolute error(MAE)=4.04 mm,root mean square error(RMSE)=5.67 mm)and high correlation(R^(2)=0.915).The thrust and depth of the tunnel were the most important factors in the prediction model influencing the upward displacement of the tunnel linings.
基金supported by the National Key Research and Development Program of China(Grant No.2020YFA0712100)National Natural Science Foundation of China(Grant No.11971325)+1 种基金supported by National Natural Science Foundation of China(Grant No.11801109)Beijing Scholars Program。
文摘For two r-graphs T and H,let ex_(r)(n,T,H)be the maximum number of copies of T in an n-vertex H r-graph.The determination of the Turán number ex_(r)(n,T,H)has become the fundamental core problem in extremal graph theory ever since the pioneering work of Turán’s theorem was published in 1941.Although we have some rich results for the simple graph case,only sporadic results have been known for the hypergraph Turán problems.In this paper,we mainly focus on the function ex_(r)(n,T,H)when H is one of two different hypergraph extensions of the complete bipartite graph K_(s,t).The first extension is the complete bipartite r-graph K^((r))_(s,t),which was introduced by Mubayi and Verstraëte(2004).Using the powerful random algebraic method,we show that if s is sufficiently larger than t,then ex_(r)(n,T,K^((r))_(s,t))=Ω(n^(v−e/t)),where T is an r-graph with v vertices and e edges.In particular,when T is an edge or some specified complete bipartite r-graph,we can determine their asymptotics.The second important extension is the complete r-partite r-graph K^((r))_(s1,s2,…,sr,)which has been widely studied.When r=3,we provide an explicit construction giving ex_(3)(n,K^((3))_(2,2,7))≥1/27n19/7+o(n19/7).Our construction is based on the norm graph,and improves the lower boundΩ(n73/27)obtained by the probabilistic method.
基金Supported by the National Natural Science Foundation of China(No.60472053)
文摘This letter gives a random construction for Low Density Parity Check (LDPC) codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has great flexible choice in LDPC code's parameters including codelength, code rate, the least girth of the graph, the weight of column and row in the parity check matrix. The method can be applied to the irregular LDPC codes and strict regular LDPC codes. Systemic codes have many applications in digital communication, so this letter proposes a construction of the generator matrix of systemic LDPC codes from the parity check matrix. Simulations show that the method performs well with iterative decoding.
