DETECTION OF THE STARTING OF THE NEWLY APPLIED MASS FOR SUCCESSIVE WEIGHING

In this study, new approaches are proposed over a range of conditions with unknown loading time to determine the initial conditions and identify the explicit model parameters of successive weighing system in the early part of the transient response. When a new mass is applied to the platform, the starting of the newly applied mass is detected by modelling error approach and then predicted automatically using the Non-Linear Regression (NLR) method and the detection process is repeated for successive continuous weighing. Simulation results are provided to indicate the improvement in both speed and accuracy of the model and the mass prediction Accurate and fast weighing is an important requirement throughout the modern \\ nJld I !-6] The platform parameters must be known for fitting the system dynamic model to thl l'arl\' pan of the platform transient response and determining the model parameters \vhieh p, ..)\ldl' the high speed mass prediction. Signal processing methods have been studied to e.I,1l1ate the weight dynamically while still in the transient mode, and more recently adaptl\'e fli',-,nng ha~ been used [1-4]. This paper presents new approach to successive continuous (non-stop) weighing. It is based on the NLR [7] signal processing approach of fItting of a lime-domain model to the early part of the dynamic weighing platform response. This method can be J;lster than the adaptive tIltering methods proposed so far because no filter adaptation time is required [5-6]. The approach is applied over a range of dynamic conditions including noisy data wit h unknn\vl1 loading time for prediction of the applied mass. This is the most ditTicult task of the th'namic weighing problem. In successive continuous weighing, when the new mass is applied to the weighing platform due to non-periodic or unknown loading time, then the starting time of the newly applied mass should be detected as soon as possible. When a new applied mass is detected, this mass is then predicted automatically using the NLR method and the detection processes are repeated for successive weight measurements [6]. The weighing platform response is governed by the solution of the second order differential equation (1) and is modelled in the most general form by a constant term and over-damped, critically-damped or under-damped transient [8-10]. ay(t) a vet) (111 + 111S ) ---+ C _0 +K Y( t) = F ( t) = f: . (111 + 111S ) a t 2 a t The speed and accuracy of mass prediction are major considerations for successive conL, I' I)~ weighing; therefore, an explicit model is developed for improved accuracy and fast mass prediction [5-6] This new model contains 5 unknown parameters, which are the applied mass 111 to be predicted, the platform parameters K and C, the initial displacement y(O) and the initial velocity y'(O) of the applied mass, where I11S is the self mass of the platform In general, weighing systems are considerably sensitive to their environments, which includes sources of noise and measurement errors affecting the accuracy of the system Tile number of unknown explicit model parameters can be reduced from 5 to 3 if the constant platform parameters K and (' are known for the given platform. The platform p:1rameters can either be found by an off-line calibration, or fllund on-line by reverting to t!w 5 parameter implicit model for a proportion of the NLR runs [6] Thus. recalibration reduces the errors induced by the environment. Assuming that any variation in I\. and (' is sl<.)"v, since the platform parameters were determined in an earlier identitlcation process, these values can be set as constant parameters for the high speed mass prediction process A further reduction in computational complexity can be obtained by estimating the initial displacement cmd the initial velocity from the d;lta by ditferent method other than the LR [5. 6. I 1-13] This can be done by fitting a polynomial curve of degree H to the data using only one iteration, "" i{ f ~ f,' (t) = L.. f ,,:1, t which is :l relatively low complexity operation. The coefficient 00 and (II give estimates of the initial disl)lacement and the velocity. These values are substituted into the explicit model, so the unknown number of explicit model parameters is reduced from 3 to I. Subsequently leaving only the applied mass to be predicted quickly by the NLR method providing accuracy and decreased computation time. Using the model equation (as given in Appendix) for the mass prediction stage therefore improving the prediction of mass significantly (see Figure I and Table-I). Displacemenl (l\:.g.) ~OOl -------~-

The approach is applied over a range of dynamic conditions including noisy data wit h unknn\vl1 loading time for prediction of the applied mass.This is the most ditTicult task of the th'namic weighing problem.In successive continuous weighing, when the new mass is applied to the weighing platform due to non-periodic or unknown loading time, then the starting time of the newly applied mass should be detected as soon as possible.When a new applied mass is detected, this mass is then predicted automatically using the NLR method and the detection processes are repeated for successive weight measurements [6].
The weighing platform response is governed by the solution of the second order differential equation (1) The speed and accuracy of mass prediction are major considerations for successive conL, I' I)w eighing; therefore, an explicit model is developed for improved accuracy and fast mass prediction [5][6] This new model contains 5 unknown parameters, which are the applied mass 111 to be predicted, the platform parameters K and C, the initial displacement y(O) and the initial velocity y'(O) of the applied mass, where I11S is the self mass of the platform In general, weighing systems are considerably sensitive to their environments, which includes sources of noise and measurement errors affecting the accuracy of the system Tile number of unknown explicit model parameters can be reduced from 5 to 3 if the constant platform parameters K and (' are known for the given platform. The platform p:1rameters can either be found by an off-line calibration, or fllund on-line by reverting to t!w 5 parameter implicit model for a proportion of the NLR runs [6] Thus.recalibration reduces the errors induced by the environment.Assuming that any variation in I\. and (' is sl<.)"v,since the platform parameters were determined in an earlier identitlcation process, these values can be set as constant parameters for the high speed mass prediction process A further reduction in computational complexity can be obtained by estimating the initial displacement cmd the initial velocity from the d;lta by ditferent method other than the LR [5.
6.I 1-13] This can be done by fitting a polynomial curve of degree H to the data using only one iteration, which is :l relatively low complexity operation.The coefficient 00 and (II give estimates of the initial disl)lacement and the velocity.These values are substituted into the explicit model, so the unknown number of explicit model parameters is reduced from 3 to I. Subsequently leaving only the applied mass to be predicted quickly by the NLR method providing accuracy and decreased computation time.Using the model equation (as given in Appendix) for the mass prediction stage therefore improving the prediction of mass significantly (see Figure I and  The present approach requires a correct sub-model selection.The model identification process has been found to be reliable if the initial guess of mass value is set to the value for critical damping [5][6] Performing one iteration of the NLR algorithm automatically identifies the correct sub-model, and then a selected explicit model is used for all subsequent iterations Therefore, the computational complexity of the NLR procedure is O(M•')=5.' a significant speed-up for high speed mass prediction by a factor of 125 is obtained.This approach provides robustness of convergence and gives accurate result-; In general, automatic weighing systems requifl~re1"lbk new applied mass on the platform r 1-6 J 1'111''; I. ,if d lcm-Icve threshold is used to detect the starting of thc applied mdSS elt II.. lit' 1,)\', ever tllcres then an increased danger of false detection due to am nUISl III Ii I ;IC second difl.cultvcan arise, if the platform is still oscillating from the Pll'\ in.1 I <III led PlaSS and <1lso If the new applied mass differs only by a c;mall amount.It can then hdppen t lat the change in amplitude of the signal due to the new applied mass is not greater than the oscillation still remaining However reliable detection the threshold must be set greater than the amplitude of the remaining oscillation, but less than the amplitude of the signal change due to the nevI applied mass [6] Hence this method can only be considered for large change in applied mass letel Ion t'the stal1ing time of the lata 11 tile j l'\ j(ll "m can be hie "I' 'CS 1I11y olle ma S (that is \\il I plainl'd in the following A more reliable way is to continuously monitor the modellintr error during the previously applied mass.It is very easy to calculate the modelling error This new approach enables to cwercome threshold approach problem, and to calculate the modelling error over a detilled data window, which constantly moves forward as time progresses [6] The window length is chosen so as to provide adequate noise averaging.A shorter window preferred to reduce calculation time.This means that a constant threshold can be set.To test this approach, simulated responses for the detection of new applied masses are given in Figures 5.

SIMULATION RESULTS
This section presents simulation results for the prediction of different applied mass values under various noisy amplitudes with unknown loading time.Simulations were carried out on a weighing system in which, K= I000 N/mm, ('=50 N/(mmls), ms=O Kg.The gravity was assumed to be K-= 1000 mm/s 2 and the mass m=100 Kg was applied at /=0.The signal was sampled at intervals of 0.02 sec.The predicted mass for noise-free data is shown in Figure 3 together with Shu's method [4] that the NLR method immediately gives the exact mass and in fact does so trOl1l sample 1r=5.The speed advantage ofNLR is clear The noise was taken to be uniformly distributed with amplitude of 2% relative to the steady state conditions.
For the noisy sign<ljthe predicted mass shows a random deviation about the exact value which diminishes with increasing numbers of samples due to the averaging effect of the model fitting.
The mass predicted by the NLR method for data containing 2% noise is plotted in Figure 4_ Predicted 11"'" (Kg.) Figure 3 Comparison of methods for noise-free data [5].
Figure 4 Weighing system displacement with noisy data and the NLR results [5].
In order to improve the accuracy of mass prediction, highly accurate values for initial velocity should be used.This can be achieved by switching from the polynomial curve fitting method to the model equation approach, providing that the mass prediction value has reached a significantly close value to the actual applied mass.
Figure 5 shows the response of the weighing platform to two consecutively applied masses, starting at 100 Kg and then adding 50 Kg.Figure 5(a) shows in more detail the effect of adding the 50 Kg to the 100 Kg.The signal is sampled at intervals of 10 milliseconds for Np= 100 samples, the time of application 100 Kg applied mass is predicted by NLR method taking only a few milliseconds.A threshold error level is set a value of 0 I that adding some safety margin on the mean squared error (MSF) of the previous model that is sufficient to indicate start of the new mass.Initially the threshold level was set to minimum value.The detection process then proceeds for the new applied mass by comparing between the previous l\lf,""/~' of the predicted 100 Kg and the present MSE of the new collected data (Nd= lOin this example, where Nd is number of test sample for detection process).
Displaccmcnt Kg.The new applied mass is indicated by significant error to an increase in MSE, over the previous steady value as shown in Figure 5(b).Here a 15% increase was used as the criterion.The previous steady value is that due to the measurement noise and would be updated at times between applies masses.
If the threshold level is too short, the method will too sensitive to individual noise fluctuations.If it is too long it is going to be come over the time.The modelling error method cannot be used, while collecting a longer data set (Np) and then performing the mass prediction process.This is because, after the new mass is being applied, the main algorithm needs longer data set and time to compute new indicated mass.During that period there is a high modelling error, therefore modelling error process should be stopped, otherwise it will falsely indicate the new mass.A tolerance level of accuracy must first be established for the particular application concerned.Therefore the sampling interval for prediction process should be taken as fairly short compared with the time constants expected for the system [9].Increasing the number of sample can improve the accuracy of the estimates but its time consuming [10, 12,13,15].
The flow chart for the implementing the approaches described in this paper is given in Figure 6.Software has been developed for successive continuous weighing, which is applicable for small to large dynamic weighing systems, provides real-time implementation.In this study, the NLR method is applied successively in modelling.identification and prediction tasks for a dynamic weighing system.The application of NLR signal processing method provides high speed parameter identification of dynamic weighing and fast prediction of the steady state value of the applied mass with significantly improved accuracy.Simulation results confirm that over a range of conditions, when a new mass is applied to the platform, the starting of the newly applied mass is detected by modelling error approach and then predicted automatically using the NLR method and the detection process is repeated for successive continuous weighing.Simulation software for successive continuous weighing ensuring realtime implementation has been used to indicate that fast and accurate results can be obtained.
t'lell eliminated from the process to obtain the upcttled Ill! dd the new mass) is present in the Signal This aSSlil lptJ( , paragraphs A conceptionally simple wa~would be to llse a lei ll11U.lcl4.(J.12. 1. 1 .1 on the platform signal, see FigLlle 2. But t\\O difficulties c, Il.1 0 J,

Figure 2 .
Figure 2. Detection of the starting of the new applied mass by threshold approach.