CN105547242A - Analysis method for measurement of tunnel arc subsidence through using transducer network - Google Patents

Abstract

The invention relates to an analysis method for measurement of tunnel arc subsidence through using a transducer network. The method comprises the following steps: S1, based on mechanical wave data, collected by a transducer, in a tunnel, establishing a wave model with respect to a change situation of mechanical waves in the tunnel, and analyzing parameters according to the change situation of the mechanical waves in the tunnel to deduce a change model of an entire harmonic wave of the tunnel; S2, through combination with generalized prediction control and according to change of wave shapes in the tunnel, predicting future change status of the tunnel; and S3, according to the prediction result, fore-warning a key point of the tunnel. The invention provides the analysis method for measurement of tunnel arc subsidence through using the transducer network.

Description

Sensor network is utilized to measure the analytical approach of tunnel Vaulted subside

Technical field

The present invention relates to a kind of analytical approach utilizing sensor network to measure tunnel Vaulted subside.

Background technology

Newly built tunnels construction and excavation inevitably causes disturbance and destruction to surrounding environment, also be certain to cause tunnel surrounding soil distortion, and then cause the inclination of tunnel upper Near Ground buildings, ftracture and even cave in, produce the Environmental Geotechnical Problems of series of complex, such as neighboring piles fracture or the larger sedimentation of generation, existing tunnel and underground utilities rupture, breakage, and pavement of road is damaged etc.

The construction in tunnel, disturbance surrounding formation will inevitably cause ground settlement and distortion, the subsider taken on a certain scale, and then the buildings or structures affecting periphery.Domestic and international tunnelling research is very extensive, particularly monitors at the scene, the research of the aspect such as model test and numerical simulation analysis is a lot, but is only limitted to the control of construction monitoring amount for the research of tunnel subsidence aspect and component values calculates.To the metering system of tunnel subsidence substantially or based on the reading of instrument, because tunnel every data measurement in real time can cause the accumulation of mass data, traditional processing mode is data vacuate and measures according to timeslice, to tunnel future entirety sedimentation and situation of change can not make and predicting accurately, therefore not enough to the early warning of accident.

Along with the progress of infotech, especially the progress of the technology of wireless sensor network, Internet of Things establishes bridge between the mankind and object, lead new information industry tide of revolution, for people's daily life brings huge change, the progress of existing sensor technology makes can carry out Real-time Collection, such as Vault settlement data, country rock grade etc. to the various measurement data in tunnel.The Real-time Collection of data brings the data of magnanimity, in order to carry out forecast analysis to the sedimentation in tunnel future, needs research based on the analytical technology of the large data of sensor Real-time Collection.

Because the analysis mode of the data in existing tunnel lacks accurate prospect to tunnel to-be, precisely can not predict the state in the following sedimentation in tunnel and prospect tunnel future, this just can not carry out early warning analysis accurately to the state in tunnel.Therefore forecast analysis is accurately carried out to tunnel subsidence, become the problem that those skilled in the art need solution badly.

Summary of the invention

In view of the above-mentioned problems in the prior art, fundamental purpose of the present invention is to address the deficiencies of the prior art, the invention provides a kind of analytical approach utilizing sensor network to measure tunnel Vaulted subside, by the dynamic change of the modeling analysis future tunnel to tunnel sensor image data, realize Accurate Prediction to tunnel subsidence, effectively can carry out early warning timely to the state in tunnel future.

The invention provides a kind of analytical approach utilizing sensor network to measure tunnel Vaulted subside, comprise the following steps:

S1: based on the data of sensor collection tunnel internal mechanical wave, the situation of change of the mechanical wave of tunnel internal is carried out volatility model modeling, the parameters of situation of change to tunnel according to tunnel internal mechanical wave is analyzed, and can derive the variation model of the overall harmonic wave in tunnel;

S2: in conjunction with generalized predictive control, according to the change of tunnel internal waveform, predicts the variable condition in tunnel future;

S3: according to predicting the outcome, can carry out early warning to the key point in tunnel.

Optionally, in described step S1, the foundation of volatility model is specially: the localized variation due to tunnel can cause the change of the entirety in tunnel, this point can use wave equation to describe the impact of tunnel localized variation on overall variation, derives the variation model of the overall harmonic wave in tunnel, namely

$\frac{\∂u(x,t)}{\∂t}=\underset{i}{\Σ}{f}_i(x,t),$

Wherein, f _i(x, t) can identify the fluctuation of tunnel local location,

the volatility model of whole tunnel entirety can be represented,

Y _it () is i-th measuring amount, f _i(x, t)=f _i(x, y (t)).

The present invention has the following advantages and beneficial effect: the analytical approach utilizing sensor network to measure tunnel Vaulted subside provided by the invention, by to tunnel sensor real time data acquisition, use the analysis of large data and excavate treatment technology and complete prospect to tunnel state, thus can Accurate Prediction to the to-be in tunnel, timely early warning can be realized.

Embodiment

Below with reference to specific embodiment, the present invention is further illustrated.

A kind of analytical approach utilizing sensor network to measure tunnel Vaulted subside of the embodiment of the present invention, by to tunnel sensor real time data acquisition, use the analysis of large data and excavate treatment technology and complete prospect to tunnel state, thus can Accurate Prediction to the to-be in tunnel, timely early warning can be realized, this process comprises three processes, that nodal community extracts respectively, attribute group ranking and checking: first based on the data of sensor collection, the situation of change of the mechanical wave of the inside in tunnel is carried out modeling.Situation each major parameter to tunnel according to the ripple of tunnel internal is analyzed; Secondly, in conjunction with generalized predictive control, according to the change of tunnel internal waveform, the variable condition in tunnel future is looked forward to; Finally, according to predicting the outcome, early warning is carried out to the key point in tunnel.

1, volatility model is set up

From physics angle, the localized variation in tunnel can cause the change of the entirety in tunnel, this point can use wave equation to describe the impact of tunnel localized variation on overall variation, can derive the variation model f of the overall harmonic wave in tunnel according to the local stress in the tunnel of sensor Real-time Collection, fluctuation, strain and displacement change _i(x, t) can identify the fluctuation of tunnel local location, the volatility model of whole tunnel entirety can be represented, that is:

$\frac{\∂u(x,t)}{\∂t}=\underset{i}{\Σ}{f}_i(x,t)---\left(1\right),$

If y _it () is i-th measuring amount, so just have f _i(x, t)=f _i(x, y (t)) so we to f _i(x, t) is as follows at the Taylor Expansion of t+ Δ t:

$u(x,t+\mathrm{\Δ})=u(x,t)+\mathrm{\Δ}t\frac{\∂u(x,t)}{\∂t}+\frac{{\mathrm{\Δt}}^2}{2}\frac{{\∂}^{2}u(x,t)}{\∂t^2}+O\left({\mathrm{\Δt}}^3\right)$

If in numerical simulation, when obtained by formula (1) macroscopic fluctuation about the first order derivative of time after, following formula can be used to obtain local variable:

$u(x,t+\mathrm{\Δ})=u(x,t)+\mathrm{\Δ}t\frac{\∂u(x,t)}{\∂t}+\frac{{\mathrm{\Δt}}^2}{2}(\frac{\∂u(x,t)}{\∂t}-\frac{\∂u(x,t-\mathrm{\Δ}t)}{\∂t})---\left(2\right)$

The form of its EVOLUTION EQUATION should be:

$f_i(x+c_i\mathrm{\Δ}t,t+\mathrm{\Δ}t)-f_i(x,t)=-\frac{1}{\mathrm{\τ}}\[(f_i\left(x,t\right)-{f_i}^{eq}\left(x,t\right)\]+{\mathrm{\ΔtS}}_i(x,t)+\frac{{\mathrm{\Δt}}^2}{2}\∂{\mathrm{tS}}_i(x,t)---\left(3\right)$

By introducing equilibrium distribution function f _i ^eqthe implicit function of (x, t), equation (3) formula can turn to as follows:

$\begin{array}{c}{f}_i(x+c_i\mathrm{\Δ}t,t+\mathrm{\Δ}t)-f_i(x,t)=\frac{1}{\mathrm{\τ}}\[(f_i\left(x,t\right)-{{\mathrm{\θf}}_i}^{eq}\left(x,t\right)\]-\left(1-\mathrm{\θ}\right){f_i}^{eq}\left(x,t\right)\]\\ +{\mathrm{\ΔtS}}_i\left(x,t\right)+\frac{{\mathrm{\Δt}}^2}{2}\∂{\mathrm{tS}}_i\left(x,t\right)\end{array}---\left(5\right)$

Therefore we can establish:

$h_i(x,t)=f_i(x,t)-\frac{\mathrm{\θ}}{\mathrm{\τ}}{f_i}^{eq}(x,t)---\left(6\right)$

According to equation (6) formula, equation (5) can turn to by we:

$\begin{array}{c}{h}_i\left(x+c_i\mathrm{\Δ}t,t+\mathrm{\Δ}t\right)-h_i\left(x,t\right)=-\frac{1}{\mathrm{\τ}}\[h_i\left(x,t\right)+\frac{\mathrm{\θ}}{\mathrm{\τ}}{f_i}^{eq}\left(x,t\right)-{f_i}^{eq}\left(x,t\right)\]+{\mathrm{\ΔtS}}_i\left(x,t\right)\\ +\frac{{\mathrm{\Δt}}^2}{2}\∂{\mathrm{tS}}_i\left(x,t\right)\end{array}---\left(7\right)$

To the h of equation (7) _i(x+c _iΔ t, t+ Δ t) use Taylor's formula to launch, equation (7) can turn to:

$D_i{h}_i+\frac{\mathrm{\Δ}t}{2}{D}_i^2{h}_i=\frac{1}{\mathrm{\τ}\mathrm{\Δ}t}(h_i+\frac{\mathrm{\θ}}{\mathrm{\τ}}{f_i}^{eq}-{f_i}^{eq})+S_i+\frac{{\mathrm{\Δt}}^2}{2}\∂{\mathrm{tS}}_i---\left(8\right)$

Wherein to the particle distribution function h in EVOLUTION EQUATION _i(x, t) about with source item distribution function S _i(x, t) is chapmanEnskog and launches to obtain:

$\begin{array}{cc}\∂t=\mathrm{\ϵ}\∂t_1+{\mathrm{\ϵ}}^2\∂t_2---\left(9\right)& \▿=\mathrm{\ϵ}{\▿}_1---\left(10\right)\end{array}$

$\begin{array}{cc}{h}_i={f_i}^{\left(0\right)}+{{\mathrm{\ϵf}}_i}^{\left(1\right)}+{\mathrm{\ϵ}}^2{{\mathrm{\ϵf}}_i}^{\left(2\right)}-\frac{\mathrm{\θ}}{\mathrm{\τ}}{f}_i^{eq}---\left(11\right)& S_i={\mathrm{\ϵS}}_i^{\left(1\right)}---\left(12\right)\end{array}$

In simultaneous equations (8) (9) (10) (11) (12), order so we can obtain zeroth order about ε to the partial differential equation of second order:

$O\left({\mathrm{\ϵ}}^0\right):-\frac{1}{\mathrm{\τ}}({f_i}^{\left(0\right)}-{f_i}^{eq})=0,$ I.e. f _i ⁽⁰⁾=f _i ^eq(13)

$O\left({\mathrm{\ϵ}}^1\right):(1-\frac{1}{\mathrm{\τ}})D_{1i}{f_i}^{\left(0\right)}=-\frac{1}{\mathrm{\τ}\mathrm{\Δ}t}{f_i}^{\left(1\right)}+{S_i}^{\left(1\right)}---\left(14\right)$

$O\left({\mathrm{\ϵ}}^2\right):\left(1-\frac{\mathrm{\θ}}{\mathrm{\τ}}\right)\∂t_2{f_i}^{\left(0\right)}+D_{1i}{f_i}^{\left(1\right)}+\frac{{\mathrm{\Δt}}^2}{2}\left(1-\frac{\mathrm{\θ}}{\mathrm{\τ}}\right)D_{1i}^2{f}_i^{\left(0\right)}=-\frac{1}{\mathrm{\τ}\mathrm{\Δ}t}{f_i}^{\left(2\right)}+\frac{\mathrm{\Δ}t}{2}{S}_i^{\left(1\right)}\∂t_1{S}_i^{\left(1\right)}---\left(15\right)$

Can obtain according to the wave equation mass conservation:

$\underset{i}{\Σ}{f_i}^{eq}=\underset{i}{\Σ}{f}_i=u_t---\left(16\right)$

Simultaneous (2) and (13) can obtain:

$\underset{i}{\Σ}{f_i}^{\left(0\right)}=u_t,\underset{i}{\Σ}{f_i}^{\left(n\right)}=u_t$ Wherein n > 0 (18)

So we can obtain according to equation (14):

$D_{1i}{f_i}^{\left(1\right)}=-\mathrm{\τ}\mathrm{\Δ}t(1-\frac{\mathrm{\θ}}{\mathrm{\τ}})D_{1i}^2{f_i}^{\left(0\right)}+{\mathrm{\τ\ΔtD}}_{1i}{S}_i^{\left(1\right)}---\left(19\right)$

Then can obtain by equation (18) formula:

$\left(1-\frac{\mathrm{\θ}}{\mathrm{\τ}}\right)\∂t_2{f_i}^{\left(0\right)}+\mathrm{\Δ}t\left(\frac{1}{2}-\mathrm{\τ}\right)\left(1-\frac{\mathrm{\θ}}{\mathrm{\τ}}\right)D_{1i}^2{f_i}^{\left(0\right)}=-\frac{1}{\mathrm{\τ}\mathrm{\Δ}t}{f_i}^{\left(2\right)}+\frac{\mathrm{\Δ}t}{2}{S}_i^{\left(1\right)}\∂t_1{S}_i^{\left(1\right)}-{\mathrm{\τ\ΔtD}}_{1i}{S}_i^{\left(1\right)}---\left(20\right)$

Can obtain i summation (19) and (20) both sides now:

$\∂t_1\underset{i}{\Σ}{f_i}^{\left(0\right)}+{\▿}_1\·\underset{i}{\Σ}{c}_i{f_i}^{\left(0\right)}=\frac{\mathrm{\τ}}{\mathrm{\τ}-\mathrm{\θ}}\underset{i}{\Σ}{S}_i^{\left(1\right)}---\left(21\right)$

$\begin{array}{c}\∂t_2\underset{i}{\mathrm{\Σ}}{f_i}^{\left(0\right)}+\mathrm{\Δ}t\left(\frac{1}{2}-\mathrm{\τ}\right)\underset{i}{\mathrm{\Σ}}{\left(\∂t_1+c_i{\▿}_1\right)}^2{f_i}^{\left(0\right)}=\frac{\mathrm{\τ}\mathrm{\Δ}t}{\mathrm{\τ}-\mathrm{\θ}}\left(\frac{1}{2}-\mathrm{\τ}\right)\∂t_1\underset{i}{\mathrm{\Σ}}{S}_i^{\left(1\right)}\\ -\frac{{\mathrm{\τ}}^2\mathrm{\Δ}t}{\mathrm{\τ}-\mathrm{\θ}}{\▿}_1\·\underset{i}{\mathrm{\Σ}}{c}_i{S}_i^{\left(1\right)}\end{array}---\left(22\right)$

The first order and second order moments of partial balancing's state distribution function applies following restrictive condition:

$\underset{i}{\Σ}{c}_i{f_i}^{\left(eq\right)}=0---\left(23\right)$

$\underset{i}{\Σ}{c}_i{c}_i{f_i}^{\left(eq\right)}=\frac{1}{\mathrm{\Δ}t(\mathrm{\τ}-\frac{1}{2})}uI---\left(24\right)$

Following restrictive condition is applied to the zeroth order square of the source item distribution function in sine-Gordon EVOLUTION EQUATION and first moment:

$\underset{i}{\Σ}{S}_i=-\frac{\mathrm{\τ}-\mathrm{\θ}}{\mathrm{\ϵ}\mathrm{\τ}}\sin u---\left(25\right)$

$\underset{i}{\Σ}{c}_i{S}_i=0---\left(26\right)$

Simultaneous (17), (21) and (24), equation (21) and (22) can turn to:

$\∂t_1{u}_t=-\frac{\sin u}{\mathrm{\ϵ}}---\left(27\right)$

$\∂t_2{u}_t+{\▿}_1\·{\▿}_{1u}I=0---\left(28\right)$

To (25) and (26) two formula ε ²the fluctuation of the entirety in tunnel can be derived by change:

$\frac{{\∂}^{2}u}{\∂t^2}-\frac{{\∂}^{2}u}{\∂x^2}-\frac{{\∂}^{2}u}{\∂y^2}=-\sin u---\left(30\right)$

$\frac{{\∂}^{2}u}{\∂t^2}-\frac{{\∂}^{2}u}{\∂x^2}-\frac{{\∂}^{2}u}{\∂y^2}=-\sin u$ Be 2 rank sine-Gordon equations.

Under the constraint of moment equation (15) (16) (26), equilibrium distribution function and source item distribution function as follows:

${f_i}^{eq}={\mathrm{\ω}}_i\[u_t+\frac{c_s^2(\frac{u}{\mathrm{\Δ}t(\mathrm{\τ}-\frac{1}{2}}-u_t)I:(c_i{c}_i-c_s^{2}I)}{2c_s^4}\]---\left(31\right)$

$S_i={\mathrm{\ω}}_i(\frac{\mathrm{\θ}}{\mathrm{\τ}}-1)\sin u---\left(32\right)$

Therefore simultaneous (17) and (26) can obtain according to above-mentioned constraint condition and (20) (31):

$u(x,t)=\frac{\mathrm{\τ}}{\mathrm{\τ}-\mathrm{\θ}}\underset{i}{\Σ}{h}_i(x,t)$

Therefore at the end of each time step develops, the first order derivative about the time of macroscopic physical quantity is calculated by formula (30), then just can calculate macroscopic quantity in future time step by formula (3), so just be derived the volatility model of tunnel change.

2, the prediction of tunnel to-be and the early warning of key point

Tunnel fluctuation change is that uncertainty mechanicalness carries out system one by one, so predictive control algorithm is when to tunnel localized variation PREDICTIVE CONTROL, is often difficult to obtain A (z in controlled equation ^-1), B (z ^-1), C (z ^-1) and D (z ^-1) parameter, be limited to the collection of sensor parameters, therefore need to set up controlled parameter in system operation, and the method needing operation parameter to estimate, On-line Estimation A (z ^-1), B (z ^-1), C (z ^-1) and D (z ^-1) parameter, therefore when controlled parameter need estimate time, following formula can be used to represent:

$\hat{A}\left(z^{-1}\right)y\left(t\right)=\hat{B}\left(z^{-1}\right){\mathrm{\Δu}}_f(t-1)+\hat{D}\left(z^{-1}\right){\mathrm{\Δv}}_f(t-1)---\left(1\right)$

In equation (1) and coefficient can be obtained by on-line identification, and what line identification parameter obtained employing usually is least square method, and concrete computation process is as follows:

$\widehat{\mathrm{\θ}}\left(t\right)=\widehat{\mathrm{\θ}}(t-1)+\frac{P(t-1)X(t-1)}{\mathrm{\α}\left(t\right)+X^T(t-1)P(t-1)X(t-1)}\×\[{\mathrm{\Δy}}_f\left(t\right)-X^T\left(t-1\right)\widehat{\mathrm{\θ}}\left(t-1\right)\]---\left(2\right)$

$\mathrm{\φ}\left(t\right)=P(t-1)-\frac{P(t-1)X(t-1)X^T(t-1)P^T(t-1)}{1+X^T(t-1)P(t-1)X(t-1)}---\left(3\right)$

Wherein in above-mentioned two equations:

$\widehat{\mathrm{\θ}}\left(t\right)={\[-{\hat{a}}_1,\mathrm{.....},-{\hat{a}}_{n_a},{\hat{b}}_0,......,{\hat{b}}_{n_b},{\hat{d}}_0,......,{\hat{d}}_{n_d}\]}^T$

X(t-1)＝[Δy _f(t-1),........,Δy _f(t-n _a),Δu _f(t-1)] ^T

$\mathrm{\α}\left(t\right)=1-\frac{1}{M\left(t\right)}$

$M\left(t\right)=1+\frac{1+X^T(t-1)P(t-1)X(t-1)}{{\[{\mathrm{\Δy}}_f\left(t\right)-X^T\left(t-1\right)\widehat{\mathrm{\θ}}\left(t-1\right)\]}^2}\mathrm{\η}\left(t\right)---\left(4\right)$

If meet following condition:

[1/ α (t)] trace [φ (t)]≤ρ is so:

P (t)=φ (t)/α (t), no person:

P(t)＝φ(t)

Selection for parameter η (t) and ρ can represent with following formula:

η (t)=m η _α(t), wherein

ρ>γ ²

In superincumbent equation, m is the length of memory, η _αt () is the variance of η (t), γ ²initial covariance matrix P (0)=γ ²value in I, and trace [φ (t)] is the mark of matrix φ (t).

When adopting the least square method line identification parameter of time-variant delays α (t), can ensure that identified parameters can the change of adaptive system stably, while can not there is again the situation that parameter identification disperses.

The generalized predictive control adaptive algorithm of performance index weighting is as follows:

Given parameters N, N _u, λ, P (z ^-1), Q (z ^-1), T (z ^-1) and parameter estimation algorithm in initial value γ, η _α, m:

(1) use equation (9)-(11) to A (z ^-1), B (z ^-1) and D (z ^-1) carry out parameter estimation;

(2) equation (5) and (7) is used to calculate with

(3) use matrix to G ^tg+ λ Ω ^tΩ inverts;

(4) equation (8) is made to calculate controlled quentity controlled variable u (t);

(5) first step is returned

Can to t according to predicting the outcome _iu (x, y, the t in moment _i) wave equation, to x _iask partial derivative, calculate and make then to each x _iinvestigate its actual fluctuation change whether to cause with expection, so early warning is carried out to this point if inconsistent.

Last it is noted that above-described each embodiment is only for illustration of technical scheme of the present invention, be not intended to limit; Although with reference to previous embodiment to invention has been detailed description, those of ordinary skill in the art is to be understood that: it still can be modified to the technical scheme described in previous embodiment, or to wherein partly or entirely technical characteristic carry out equivalent replacement; And these amendments or replacement, do not make the essence of appropriate technical solution depart from the scope of various embodiments of the present invention technical scheme.

Claims (2)

1. utilize sensor network to measure an analytical approach for tunnel Vaulted subside, it is characterized in that, comprise the following steps:

S1: based on the data of sensor collection tunnel internal mechanical wave, the situation of change of the mechanical wave of tunnel internal is carried out volatility model modeling, the parameters of situation of change to tunnel according to tunnel internal mechanical wave is analyzed, and can derive the variation model of the overall harmonic wave in tunnel;

S2: in conjunction with generalized predictive control, according to the change of tunnel internal waveform, predicts the variable condition in tunnel future;

S3: according to predicting the outcome, can carry out early warning to the key point in tunnel.

2. the analytical approach utilizing sensor network to measure tunnel Vaulted subside according to claim 1, it is characterized in that, in described step S1, the foundation of volatility model is specially: the localized variation due to tunnel can cause the change of the entirety in tunnel, this point can use wave equation to describe the impact of tunnel localized variation on overall variation, derive the variation model of the overall harmonic wave in tunnel, namely wherein, f _i(x, t) can identify the fluctuation of tunnel local location, the volatility model of whole tunnel entirety can be represented, y _it () is i-th measuring amount, f _i(x, t)=f _i(x, y (t)).