Mohamed Sameh Belaid
email: mohamed-sameh.belaid@imt-lille-douai.fr

Stéphane Lecoeuche
email: stephane.lecoeuche@imt-lille-douai.fr

Anthony Fleury
email: anthony.fleury@imt-lille-douai.fr

Baptiste Hervé
email: baptiste.herve@fr.bosch.com

-Morocco "New advances and challenges for sustainable and smart industries" IMPROVEMENT OF SALES PREDICTION BY FITTED-TO-PRODUCT TIME-SERIES MODELS

Keywords: Industry 4.0, Supply Chain, Machine Learning techniques, Data Analytics, Time Series

In this paper, we present an application of machine learning models with real-world data in order to enhance a company's performance. First, we present a brief literature review about the new trends in the field of supply chain predictive analytics and about the models used during this case study. We present then the industrial data-driven models to improve the overall supply chain performances in the scope of the Sales and Operations Planning (S&OP) process. We will present in our work, the considered assumptions and the methodology developed in order to implement a sales prediction engine, through several time series forecasting models. In this work, we use and mix classic time series models like ARIMA and Exponential Smoothing, and the recent Prophet algorithm. Finally, we present the results of the implementation of our methodology and the noted improvements on the predictions accuracy. Our discussions derive on how predicting customer demand for many products from different natures and on how the model parameters affected our sales forecasting process.

INTRODUCTION

In an economic world characterized by increased competition, companies are still seeking to strengthen their competitiveness in order to gain a foothold in the market. To achieve this goal, several areas of development are considered, among which, the improvement of the supply chain through exploiting emerging data-driven techniques.

Our paper is related to an industrial application seeking for improving the industrial performance of the company elm.leblanc (subsidiary of Bosch Group and a French market leader in the heating systems industry). We aim to implement innovative methods around data-driven modelling, which will ensure better management and efficiency of the supply chain.

In order to reduce storage costs and effectively plan the company production, we realized investigations and diagnostics over the Supply Chain stockholders. A common point reported is the poor quality of sales forecasts as it is the first step in the Sales & Operations Planning process (will be discussed later) and the conductive phase of the rest of the Supply Chain.

The sales prediction task represents multiple complexities due to the influence of internal and external environments [START_REF] Sun | Sales forecasting using extreme learning machine with applications in fashion retailing[END_REF] such as the diversity of the products, the several variables that could affect the sales and the various non-linear patterns that can be represented in the data. Added to that, a huge data volumes are generated leading to difficulties in manually making accuracy forecasts. In order to raise these challenges, machine-learning techniques are considered as interesting approaches and suitable methods to deal with such data [START_REF] Cheriyan | Intelligent Sales Prediction Using Machine Learning Techniques[END_REF] through extracting useful information and insights. To respond to this industrial need, we investigate the state-of-the-art data-driven models and exploit them to implement a sales prediction engine.

Our proposition consists in a scalable methodology which aims to improve sales forecasting through selecting the accurate model for each product based on several assumptions. This is motivated by the fact that products have specific sales signatures and trends. These works illustrate an industrial experience of implementing a machine learning approach with real-world data. The purpose is to reduce costs, enhance planning processes, improve inventory management and optimize the overall supply chain to satisfy customer demand.

In this paper, we present a brief literature review about the new trends for supply chain improvements coupled with the S&OP process and its relation with these trends. We also present a literature review about different models used for time series forecasting. Then, we will introduce the framework application and the followed methodology in order to implement an accurate prediction engine for a variety of products and sales patterns. Finally, we discuss the results and experiments and our future intended works.

MOSIM '20 -November 12-14, 2020 -Agadir -Morocco

SUPPLY CHAIN PREDICTIVE ANALYTICS

Sales & Operations Planning (S&OP)

The S&OP process is an integral process that aims to balance supply and demand, and to make the link between the company's strategic and its operational plans (Thome et al., 2012a). These objectives are achievable through the deployment of a vertical alignment between the planning levels (strategic, tactical, operational) (Thome et al., 2012b) as well as a horizontal alignment between the different functions of the company or interfunctional alignment. This process typically involves five steps as shown in the following figure 1.

Figure 1: The S&OP process According to [START_REF] Wallace | The Demand Planning Process in Executive S&OP[END_REF], the demandplanning step can be the most challenging within the five steps of the S&OP for many companies. This step is preceded (and strongly influenced) by the demand forecasting, in which statistical techniques are used. [START_REF] Lapide | S&OP: The Linchpin Planning Process[END_REF] stresses the importance of the demand forecasts for the smooth running of the S&OP process since the plans are driven by it. [START_REF] Wang | Big data analytics in logistics and supply chain management : Certain investigations for research and applications[END_REF] affirm that there are two widely quantitative techniques used in supply chain analytics which are "times-series analysis and forecasting" and "regression analysis". The first aims to determine existing patterns in historical data and predicts future events based on that, and the second intends to understand relationships and causality between variables. Beyond these classic methods, several models are developed by associating other machine learning techniques like Artificial Neural Networks. The rest of the paper is devoted to that objective, requesting the use of efficient time series modelling techniques.

New trends and field of research

Recent works on Supply Chain Management (SCM) field are interested in the integration of new technologies derived from Data science such as big data and predictive analytics. These trends bring out new opportunities for professionals. [START_REF] Waller | Click Here for a Data Scientist : Big Data , Predictive Analytics , and Theory Development in the Era of a Maker Movement Supply[END_REF] suggest different definitions and concepts in this purpose, namely, SCM Predictive analytics and SCM data science. They are defined as the application of advanced analytic techniques including data mining, statistical analyses and predictive analytics on big datasets [START_REF] Tiwari | Big data analytics in supply chain management between 2010 and 2016 : Insights to industries[END_REF]. They bring more possibilities to create data-driven decision-making tools in order to improve supply chain profitability.

In this context, our works focus on a new contribution of SCM predictive analytics in the objective to improve the operation planning decision process by the means of a better understanding and a better prediction of the demand. The next section gives an overview of models, used for predictive analysis and time series forecasting.

TIME SERIES FORECASTING MODELS

Time series, is a sequence of data points representing the evolution of a quantity over time, such as product sales. This area has attracted the attention of researchers over last few decades due to its different applications, especially in economy, finance, retail and industry. Time series forecasting fits under supervised machine learning problems and specifically regression ones. It aims to determine the way in which time series are changing by describing the relationship between its historical data points and/or other explanatory variables through a mathematical model. Several models were developed in the literature in order to model and predict time series. We present hereafter the models that were studied and used in our approach.

ARIMA and Seasonal ARIMA

ARIMA, which stands for Autoregressive Integrated Moving Average, is a linear forecasting model mainly used for stationary time series prediction [START_REF] Panigrahi | A hybrid ETS-ANN model for time series forecasting[END_REF] .i.e. time series with time independent properties such as mean and variance. It is a combination of autoregressive (AR) and moving average (MA) models, with a term of differencing (I) used to overcome the non-stationarity of some time series. ARIMA is characterized by (p,d,q) parameters which are respectively, the number of lag observations, the size of moving average window and the number of times to differentiate the time series in order to make it stationary. ARIMA can be expressed [START_REF] Hyndman | Forecasting: principles and practice, 3rd edition[END_REF] as the following equation (1):

MOSIM '20 -November 12-14, 2020 -Agadir -Morocco (1) Where is the data values at time t, an identically distributed random error with a null mean and a constant variance, and are respectively the Auto Regression and the Moving Average coefficients. A backshift operator B defined as .

The most important phase in the process of forecasting using ARIMA model is identifying the best parameters that lead to well fit the data and provide forecasts with a good accuracy. In the literature, different methods are proposed to find these parameters. The most popular way is to follow the Box-Jenkins methodology [START_REF] Box | TIME SERIES ANALYSIS : Forecasting and Control[END_REF]. It relies on an iterative approach of identifying a model, estimate its parameters and diagnostic checking to determine the best model. The choice of models is generally based on ACF (autocorrelation function), PACF (partial autocorrelation function), AIC (Akaike Information Criterion) or BIC (Bayesian Infor-mation Criterion) calculation. Another method is to simply try all possible values of the parameters through a grid search and then compare them by a metric like AIC.

A more intelligent and automated method is the Hyndman-Khandakar algorithm described in [START_REF] Hyndman | Forecasting with Exponential Smoothing -The State Space Approach[END_REF]. It is an automated process of best order identification through combining unit root tests, minimization of the AICc (corrected AIC) and MLE (Maximum Likelihood Estimation) (Hyndman, R.J. Athanasopoulos, 2019).

In the Seasonal ARIMA extension, additionally to the (p,d,q) ARIMA orders, (P,D,Q,m) orders represents the seasonal part of the model. "P" represents the seasonal autoregressive order, "Q" represents the seasonal moving average order, "D" is the seasonal difference order and "m" is the seasonal period of the time. SARIMA can be expressed through the following equation ( 2):

(2)

Where of order P and of order Q are respectively the seasonal Auto-Regression and the seasonal Moving Average coefficients, and B the backshift operator. Comparing to ARIMA model, SARIMA(p,d,q) (P,D,Q,m) has more possible combinations, and in order to fit the best model, the parameters can be chosen through the same methods presented before for ARIMA.

Exponential Smoothing

Exponential smoothing models are classical time series forecasting models widely used in business and industry [START_REF] De Gooijer | 25 years of time series forecasting[END_REF]. They include 24 different variants presented in [START_REF] Hyndman | A state space framework for automatic forecasting using exponential smoothing methods[END_REF]. Simple exponential smoothing consists in calculating future values based on weighted averages of past values with an exponential decreasing of the weights. It is characterized by an α parameter representing a forgetting factor (Hyndman, R.J. Athanasopoulos, 2019) i.e. the importance that will be given to the last observation. It is usually used with data representing no trend and no seasonality patterns, to predict the level i.e. the average value of the series.

This model was improved later with [START_REF] Holt | Forecasting seasonals and trends by exponentially weighted moving averages[END_REF] works, adding the capacity of detecting the trend component in the time series through adding another component with a second parameter β. This is known as double exponential smoothing model with constant trend. The works of [START_REF] Gardner | Exponential smoothing: The state of the art[END_REF], [START_REF] Taylor | Exponential smoothing with a damped multiplicative trend[END_REF] proposed to model a "damped" trend through introducing a damping parameter ϕ able to capture a constant long-term evolution, which forces the trend to converge to a constant value in the long-term future.

Through adding a seasonal component, the triple exponential smoothing comes with two variants: additive and multiple seasonality components (Hyndman, R.J. Athanasopoulos, 2019). The seasonal effect is determined through an exponential weighting method with a learning rate γ. (Hyndman, R.J. Athanasopoulos, 2019) presented in their book the different taxonomies and formulas of level, slope and seasonality calculation. The following equation (3) presents an example of an exponential smoothing model with additive trend and seasonality:

(3) Where , , and represent respectively the predicted values, the level, the slope and the seasonal component of the series at time t. h denotes the number of predicted periods and k is the integer part of m is the frequency of seasonality. The choice of the best parameters (α, β, ϕ, γ) is done by the analyst or fitted automatically by an optimization tool. In the most of the cases, the selection is based on maximizing of the likelihood i.e. the probability of the data arising from the specified.

Prophet

Recently, [START_REF] Taylor | Forecasting at Scale[END_REF] published a new forecasting model based on the Generalized Additive Models (GAM) [START_REF] Hastie | The Elements of Statistical Learning Data[END_REF]. GAMs are recently used in the data science field [START_REF] Larsen | GAM: The Predictive Modeling Silver Bullet[END_REF]. They represent an interesting model structure thanks to their interpretability, flexibility and automation with the predictors' capacity to model different behaviours. Based on this approach, Prophet model was proposed by the research team of Facebook in order MOSIM'20 -November 12-14, 2020 -Agadir -Morocco to predict time series. The model is composed from three main components: trend, seasonality and holidays as presented in the equation ( 4).

(4)

The trend can represent a nonlinear behaviour by the mean of a piecewise logistic growth model, and a linear one through a piecewise linear model. An interesting feature in trend modelling is the "change points" aspect where the user can specify special date points where trend may change according to his knowledge on the time series. The seasonality aspect is modelled through a standard Fourier series that can handle yearly, monthly and weekly seasonality. The Prophet model can handle additive or multiplicative seasonality in the time series. The third component represents holidays or special events modelling.

Machine learning approach

Several works are presented in the literature on solving sales prediction task with machine learning techniques. In [START_REF] Cheriyan | Intelligent Sales Prediction Using Machine Learning Techniques[END_REF], authors evaluate the performances of three models: generalized linear model, decision tree and gradient boosted tree, and select the best algorithm to make sales prediction for an e-fashion store. In the same idea, [START_REF] Gumani | Forecasting of sales by using fusion of machine learning techniques[END_REF] compare various machine learning models namely XGBoost, Support Vector Machines (SVM) and Regressive Neural Network (ARNN) with ARIMA, hybrid methods and STL decomposition based methods in order to figure out the most model to forecast drug store company sales. They concluded that non-linear models such SVM and XGBoost performed better than ARIMA, however, hybrid models gave better performances than individual ones. Added to that, STL decomposition based methods gave the results in terms of prediction accuracy.

An interesting approach has drawn attention in the recent years by combining multiple machine learning models to make final predictions. [START_REF] Punam | A twolevel statistical model for big mart sales prediction[END_REF] present in their works a two-level model for sales forecasting. First, predictions are made individually by the different models such as linear regression and support vector regression (SVR). Then, these predictions are combined using another model such as cubist to make more accurate final predictions. In the same idea, [START_REF] Pavlyshenko | Machine-Learning Models for Sales Time Series Forecasting[END_REF]) implement a multilevel model composed of several machine learning models, and the final predictions are generated through summing weighted results of the last level.

Other approaches

Other interesting approaches also exist in the state of the art and has recently emerged. Long Short-term Memory (LSTM) represents a successful application of the Artificial neural networks (ANN) for time series forecasting (Pankaj [START_REF] Malhotra | Long Short Term Memory Networks for Anomaly Detection in Time Series[END_REF]. However these models present some inconvenient especially their complexity and over-parameterization [START_REF] De Gooijer | 25 years of time series forecasting[END_REF]. In addition, generally, they need very long time series to produce good forecasts, so that for short-time series, classic methods perform better.

Another approach emerged recently through the use of hybrid methods through combining linear and nonlinear models such as ARIMA with ANN in [START_REF] Zhang | Time series forecasting using a hybrid ARIMA and neural network model[END_REF] works, or combining Exponential Smoothing with ANN models [START_REF] Panigrahi | A hybrid ETS-ANN model for time series forecasting[END_REF].

Several works in the literature have proved that classic methods such as ARIMA and Exponential Smoothing outperform ANN [START_REF] Gorr | Comparative study of artificial neural network and statistical models for predicting student grade point averages[END_REF]. However, others have demonstrated that ANN are more accurate in terms of forecasting [START_REF] Aras | A new model selection strategy in time series forecasting with artificial neural networks: IHTS[END_REF]. Actually, these results depend on the application, the type, and the length of the time series in question. For our case, we are treating univariate noisy time series that are more or less short (60 data points at maximum). Therefore, ANN will not deliver accurate results as stated due to the lack of long-time series data. Added to that, our data may represent linear behaviour that can be modelled with ARIMA and simple or double exponential smoothing, and nonlinear patterns that can be modelled through Triple exponential smoothing or Prophet. Based on these facts, we decided to use classical models to implement a prediction engine for all our time series.

PROPOSED METHODOLOGY

Data preparation

Our first step is the data collection. It is represented by the sales information such as the quantities, products, type of customers, products family, etc. from 2015 until the end of 2019. Data are gathered from different sources namely the enterprise resource planning system, marketing department and sales department. These data are merged together and aggregated to construct time series representing monthly quantities per product. Then, the whole dataset of time series is fed as input to the algorithms as explained later in the methodology.

Assumptions

Our time series represent sales quantities of several products per month. Some products present seasonal patterns, however, others do not and these products belong to different families, which lead to different nature of time series. Another challenge is that some products have been recently launched, so with short time series and others that are older with longer time series.

MOSIM '20 -November 12-14, 2020 -Agadir -Morocco As [START_REF] Hyndman | Minimum sample size requirements for seasonal forecasting models[END_REF] explained in their article, the use of seasonal models requires a minimum number of observations on the data since they should be at least larger than the number of parameters by one. They highlight that the use of Holt-Winters method for example, requires at least 17 observations for monthly data, and for SARIMA(0,1,1)(0,1,1)12 at least 16 observations. Additionally, the randomness and variations also require more data to fully capture the patterns in data. Based on these statements, we decided to separate our data into two groups: short time series with fewer than 24 observations to be forecasted with non-seasonal models, and long-time series with more than 24 observations can be forecasted using seasonal models.

As mentioned in (Hyndman, R.J. Athanasopoulos, 2019), exponential smoothing methods with multiplicative trend tend to produce poor forecasts quality, however, (McKenzie and Gardner, 2010) argue that a damped multiplicative trend has performed well in numerous empirical studies. In addition, during experiments we found that for some time series a multiplicative trend produce better forecasts than other models, so we decided to keep some multiplicative trend models in the prediction engine.

The proposed methodology helps to forecast several products with different models, and as was expected, algorithms do not behave in the same way for all products. The modelling stage consists in fitting the best model for each product, model that outperforms the others. Based on these findings and assumptions, the following methodology was developed to implement the forecasting engine for the different products.

Methodology

The following diagram (figure 2) represents our global forecasting methodology: Then, the trained model with optimized parameters will be used to forecast the N periods. The most important step is the model type selection that will be explained hereafter. For the next stage, the trained models are in competition during the testing phase in order to choose the best model structure with respect to the following equation:

(5)

The error metric is used to identify the winning model. In our model selection, we used the Root Mean Squared Error (RMSE) [START_REF] Chai | Root mean square error (RMSE) or mean absolute error (MAE)?[END_REF] in order to select the best model for a given time series. RMSE is defined as:

(6) Where are the observed values, the predicted values and n the number of observations. The choice of the best model type for each product depends, actually, on the number of periods given by the user to be forecasted. In fact, if the user asks for onemonth (one-step) forecasting, that means that we should choose the best model for short-term prediction. In this case, the selection procedure is done using the walkforward (back testing) technique: we fit a model on a training data until the period t and we predict the t+1 period. Then, the predicted t+1 period will be compared to the real t+1 value from the testing set to save the error. Later, we add this real value to the training dataset and refit the model. We continue this process until we finish all the test dataset. In the case where the user asks for mid or long-term forecasts, the test is done directly overall the test set. In both cases, the model structure with the minimal RMSE will be chosen to make predictions.

The implementation of the different algorithms is done in Python using stats models library for Exponential Smoothing models, pmdarima library for ARIMA and SARIMA models and the fbprophet package for Prophet model.

EXPERIMENTS OF INDUSTRIAL USE CASE

Framework and experiments

These works are conducted within elm.leblanc company in their Research and Development department. To perform different experiments, we gathered sales data represented by time series of all components, products and spare parts from data warehouse. In order to simplify the context application, we decided to focus our works on a limited perimeter represented by the top sold accessories and by the wall boilers products assembled in one plant, for the French market. These boilers represents 80% of the sales, and bring the most profitability to the company. The sales are composed of three product types among them there are different product families and among every family several products considered as time series. To make forecasts, the data is split in training and testing datasets using 90% to train models and 10% to test them. In our use case study, we have monthly time series data of different natures (stationary or not) and lengths (60 months for old products to 16 months for recent ones).

The approach presented in 4 has been applied on the 316 different products using real-world data to make midterm (3 months) and short-term (1 month) predictions. Before presenting the impact of these experiments, we are interested to see how products are gathered by model type in order to more understand and categorize our time series based on forecasting models. This identification can lead to create a sort of product groups, study the similarities presented in these time series and obtain a better understanding on the product sales in order to improve forecasts.

For midterm forecasting, the table below presents the repartition of the products modelled by each model.

Models Modelled products

Prophet 40 products

ARIMA/SARIMA 43 products

Exponential Smoothing 233 products Table 1: Number of products for each model

We found that Prophet model was selected for 40 products which are time series representing almost a similar pattern. Figure 4 presents examples of the sales of these products.

MOSIM'20 -November 12-14, 2020 -Agadir -Morocco Most of the products represent a recognizable seasonal behaviour presented by decreasing sales in August from each year and an important increase on the quantities in the end and the beginning of each year. Prophet succeeded in capturing the variability on these products better than other models. Therefore, this example supports our methodology in choosing suitable model for each time series and not to apply one model for all products.

The ARIMA model was used for 24 products representing different behaviours but we found that some products having a special behaviour is well captured by ARIMA as presented in the next figure 5. We notice that this type of product presenting an important increase on sales quantities in the end of 2018 was well captured by ARIMA than by other models. Also, these time series do not represent strong seasonal patterns which justify why ARIMA performed over other seasonal models.

The most used model type were Exponential Smoothing (ES) techniques, they were selected for 233 time series, with different components. 12 Exponential Smoothing models competed make forecasts with multitude combinations. We noticed that a model with additive trend (damped or not) was the most selected over other ES models and other models types with 141 products, which explain that most of the products have a slowly increasing trend. Some products do not present a trend, so a pure seasonal model won the competition. However, others with important trend are modelled through a multiplicative trend and a seasonal component. As we can also see, many products are modelled through an additive seasonal component, which also explains that from year to another, the seasonal pattern do not increase rapidly.

Comparing these products to others modelled by Prophet and ARIMA/SARIMA, we notice some differences between time series. Those with a clear trend but little variability were almost modelled with a double exponential smoothing. Other times series representing an important seasonality but no trend pattern was almost modelled with a simple exponential smoothing model. The figure below represents examples of products modelled with a double exponential smoothing with a multiplicative damped trend. Through these examples, we can explain why a model can be used for a time series and not for another, which justify the importance of using several models in our sales forecasting methodology.

For short-term predictions, we applied this methodology also to predict 3 months, one month each time. The model type selection differs from month to month and we do not find the same model taxonomy as for the midterm predictions. This fact also justifies, our interests on using different models since while we evolve on time, MOSIM'20 -November 12-14, 2020 -Agadir -Morocco we get more data and the time series patterns and behaviours can change according to external factors. Therefore, this methodology permits this prediction engine to be scalable over time.

An interesting aspect also noted is that products that belong to the same product family are modelled with different methods, which prove their different natures and the necessity to be treated separately.

The next paragraph will present the impact on company sales forecasting after implementing and running the algorithms

Methodology Impact on company sales forecasting

In the following graph (figure 7), we present a sample of different products histogram of sales versus models forecasts versus sales department forecasts for the last trimester of 2019, and then we will present an example of the results on the top four sold boilers. We note first that the actual method used in the sales department for forecasting is done manually and it is based on the intuition and the customers' demands. As we can notice, for several products models outperform the actual forecasts especially for products with important quantities. However, for some products models were less powerful. These products are generally recently launched, so with short time series.

In the following table 3, we present a sample of results on the top four sold boilers and we present the forecasting errors of the models and the sales department. In the last row, we present the total of absolute errors over all boilers for both horizons also.

Table 3: Forecasts errors comparison for short and midterm.

We also studied the 4 boilers that were the most erroneously forecasted by the sales department and, surprisingly, they were the same products that are the most sold.

As we can understand from the tables, our methodology outperformed sales department in 3 products in both horizons and sometimes with much less error. Models were less good on one product which presented huge variability over years.

As we can see, for many products, we could have an important improvement especially that among them there are "high runner" products, which means important quantities and then important cost saving specially in storage. However, the models did not well performed for some other products and this especially due to either lack of data for the recently launched ones, or for unpredictable events such as unexpected shutdowns or other external factors that may influence the sales.

The table mentioned above is an example of the results that we had and it does not represent the whole products studied. However, the overall noted improvements will be discussed in the next paragraph.

The overall improvement rate for all products in the midterm is 12 % compared to actual forecasts made by sales department. Moreover, for the short-term forecasting, we estimate an improvement rate by 15 % for all products.

One can say that this represents a small improvement but these are significant improvements compared to the volume and the value of the products and the storage costs. More, these results are based only on historical data, with some lacks of data and without taking in consideration any other external or internal data. In this work, we considered to avoid the use of external data. As an example, commercials are in a direct contact with customers and can bring explanatory factors. In its industrial application, we plan to integrate this additional information in our proposed methodology in order to improve our models and our forecasts. In addition, the presented work will be improved through multiple ways that will be discussed in the perspective section.

MOSIM '20 -November 12-14, 2020 -Agadir -Morocco From a managerial point of view, the sales forecasting tool has improved the efficiency of the S&OP process through enhancing the demand-planning step by bringing an additional information captured from the data. It provides a solid base to conduct discussions in this most challenging step of the process. An accurate demand plan will facilitate the development of production and replenishment planning, and the control of inventory costs.

CONCLUSION & PERSPECTIVES

In this paper, we made a literature review on supply chain analytics field and the potential applications of emerging technologies such as machine learning and data mining to improve supply chain processes. A specific process on which we have focused is the Sales & Operations Planning. We then proposed a way to improve the implementation of such process through the enhancing the sales prediction step. In this purpose, we studied several models used for time series forecasting and we proposed a new methodology to select the best structure model according to the type of product sales. This is justified by the fact that even the products could be seen as similar, in a wide product catalogue, each product has specificity in terms of sales. We designed a prediction engine following the developed methodology in order to make forecasts for several products with different natures. The results seem to be very encouraging since we note a good progress in terms of global prediction accuracy compared to the existing methods. In order to reduce the scope, we performed the different experiments on specific products. These preliminary results represent a gain of performance and a success for the company but the methodology has to be extended to other products and components. This represents a challenge since there have dozens of thousands of time series to forecast.

These preliminary results can be improved through different ways. In these works, the main limitation is related to the selection of a unique "best model". As improvement, a decision procedure could be added in order to compare scores for several models. We can use a cooperation/competition of model results in order to define clusters of products that have similar sales model structures, and to provide forecasts with more accuracy. In addition, the data granularity can be increased through using weekly data instead of monthly data then aggregate the results. This may enlarge the time series length, which let us use models that are more sophisticated. Also, other external factors that may influence the sales of the products have to be studied and then multivariate time series models could be requested.

Figure 2 :

 2 Figure 2: Global forecasting methodology

Figure 3 :

 3 Figure 3: Model type selection methodology

Figure 4 :

 4 Figure 4: Examples of products modelled by Prophet.

Figure 5 :

 5 Figure 5: Examples of captured behaviour by ARIMA

Figure 6 :

 6 Figure 6: Examples of products with multiplicative damped trend

Figure 7 :

 7 Figure 7: Sales VS Models Forecasts VS Sales Department Forecasts.

Table 2 :

 2 Table 2 summarizes the repartition of the products by model. Number of products for each ES model

				Seasonality
			None	Addi-tive	Multiplica-tive
		None	-	47 pdts	-
	Trend	Additive	81 pdts 50 pdts	10 pdts
		Multiplicative 24 pdts	9 pdts	12 pdts


est destinée au dépôt

The "Mantamaran", a light, robust, portable and affordable sampler designed for altitudes lake microplastics sampling campaigns

Frédéric Gillet, Peter Gallinelli, Emmanuel Naffrechoux, Johnny Gasperi,

David Gateuille

To cite this version:

Frédéric Gillet, Peter Gallinelli, Emmanuel Naffrechoux, Johnny Gasperi, David Gateuille. The "Mantamaran", a light, robust, portable and affordable sampler designed for altitudes lake microplastics sampling campaigns. MICRO 2020, Fate and Impact of Microplastics : Knowledge and Responsabilities, Nov 2020, Arrecife (on line), Spain. hal-02981252

The "Mantamaran", a light, robust, portable and affordable sampler designed for altitudes and remote lake microplastics sampling campaigns To monitor lake surfaces, the "Mantamaran", a contraction of manta net and catamaran, was developed for the purpose.

The main advantage of this boat is to be able to collect representative samples over the entire surface of the lake.

The Mantamaran (credits photo Marie Raison)

MICRO 2020 : Fate and Impact of Microplastics : Knowledge and Responsabilities, Lanzarote, Espagne, 23 au 27 novembre 2020

The "Mantamaran" is a light, robust and portable sampler specially designed for campaigns on altitude and remote places.

Equipment

The "Mantamaran", is composed of two inflatable kayaks, a metal structure, and some special equipment and is designed to be assembled on site. Four to five persons are required to carry the equipment (60 kg).

Since sampling cannot be achieved while paddling, the raft is propelled by a non-polluting electric motor. The electric motor and lithium-ion battery package were specifically designed for the project by SHEMATIC (www.shematic.ch), and a compromise weight versus power was achieved to allow at least three runs in the same campaign.

This device incorporates a 50 µm removable mesh net designed specifically for this special craft.

A compromise was made between mesh dimensions and propulsion power, to limit drag force and avoid mesh tear.

A logging device was developed by HEPIA (www.hesge.ch/hepia) including a GPS system and several sensors (flow sensor, sonic sensor, temperature) that allow for high accuracy of the measurements. Special attention has been paid to the measurement of flow velocities and water heights into the net in order to properly determine the filtered water surfaces and volumes.

Experience feedback

The boat, propelled at a speed of about 1 knot, allows filtering of volumes between 100 and 200 m 3, depending on sampling times.

The raft has been tested and optimized in various and challenging conditions. It offers excellent stability, buoyancy and safety with a payload of up to four persons and scientific equipment.

Due to its small dimensions (360 cm x 250 cm), the boat is very manoeuvrable and can be used in complex conditions to avoid shoals and ice floes. The electric propulsion system is retractable and can be easily removed.

Our work has shown that estimating the filtered volumes from the speed of the boat, as it is often done, instead of the real flow velocities within the net induces an overestimation by a factor of up to 2 or 3, which has direct consequences on the estimated concentrations of microplastics. In addition, the calculation of the ratio between the speed of flow in the net and that of the boat's advance makes it possible to set an objective criterion for monitoring the net clogging which constitutes a major bias in the contamination estimation. Indeed, the clogging of the net induces the backflow of the surface water layer and the loss of floating microplastics. AQUALTI NGO will be happy to give you more information or to carry out sampling campaigns in remote environments in any place in the world.

Frédéric GILLET 1 , Peter GALLINELLI 1 , Emmanuel NAFFRECHOUX 2 , Johnny GASPERI 3 , David GATEUILLE 2 Afilliations 1 AQUALTI 73000 CHAMBERY (France) 2 EDYTEM, UMR 5204 CNRS -Université SAVOIE MONT-BLANC 73000 CHAMBERY (France) 3 IFSTTAR Université GUSTAVE EIFFEL 44344 BOUGUENAIS (France)

	The presence of microplastics in the oceans is deeply documented and is the subject of numerous
	investigations and publications. Research on microplastics in fresh water, especially in mountainous
	and remote locations, however, is very poorly documented.

In this context, a research programme called PLASTILAC (www.aqualti.org/plastilac) involving NGO AQUALTI and research teams (University SAVOIE MONT-BLANC, University GUSTAVE EIFFEL) was launched to measure microplastics in alpine altitude lakes in the French Alps and to confirm the possible presence of microplastics in areas far away from sources of pollution. Access is generally possible by helicopter or by foot only and requires a light weight. Nine mountain lakes in altitudes above 1800 m were monitored in 2019 and 2020.


Marie-Christine Gromaire
email: marie-christine.gromaire@enpc.fr.

Sylvie Barraud
email: sylvie.barraud@insa-lyon.fr.

Fabrice Rodriguez
email: fabrice.rodriguez@ifsttar.fr.

Alexandre Bak

Philippe Branchu

Hélène Castebrunet

Kelsey Flanagan

Robin Garnier

Pascale Neveu

Julien Paupardin

Gromaire Mc

Branchu Ph

La gestion alternative des eaux pluviales permet-elle une maîtrise efficace des flux de micropolluants? Retour d'expérience des projets Matriochkas, MicroMégas et Roulépur

Keywords: Micropollutants, Monitoring, Runoff, Stormwater Control Measures, Treatment

teaching and research institutions in France or abroad, or from public or private research centers.

INTRODUCTION

Urban runoff is known to be a significant source of diffuse pollution of aquatic environments. Its contamination has been widely documented for several trace metals, hydrocarbons and PAH. It is also a source of less documented organic micropollutants, such as plasticisers, surfactants, biocides and flame retardants (Gasperi et al 2014). In view of the limits of centralized treatment solutions, alternative stormwater management and source control of urban runoff are widely promoted today (Fletcher et al 2014). Some of these stormwater control measures (SCM) are mainly designed for hydrologic management while others specifically target depollution objectives. However the efficiency of these solutions for micropollutant load reduction, as a function of the type and size of the contributing watershed, is still insufficiently documented. This is all the more difficult as the nature of urban runoff and the extent of its contamination may vary greatly depending on catchment characteristics.

The present communication is based on a pooling of results from three French research projects (Roulépur project in Greater Paris, Matriochkas in Nantes metropolitan area and MicroMégas in Metropolitan Lyon), funded by the French Biodiversity Agency and the Water Agencies, under the same national call on "Innovations and changes in practice: Control of micropollutants in urban water". All three focused on in-situ evaluations of the performance of various urban runoff management structures, from both the hydrologic and pollutant load point of view.

METHODOLOGY

A total of 12 SCMs were studied on 9 different sites over the 3 projects ( Table 1). They cover a wide range of solutions, from very diffuse implementation (pervious parking lot, vegetated filter strip, infiltration or bioretention swale, infiltration trench, compact industrial product) to more centralized ones (dry and wet ponds). The ratio α between the surface of the SCM and the impervious surface of the catchment ranges from almost 0% to 100%. Only 4 out for the 12 devices have been specifically designed for depollution, i.e. reduction of pollutant concentrations (compact industrial product, sand filter, bioretention swale and vegetated filter strip), while the other ones were initially intended for hydrological runoff management (pervious parking, infiltration trenches or swales, detention or retention basins), even if some retention processes are intrinsically present in these systems. The studied catchments included a variety of roads and car parks, as well as an industrial catchment and a mixed urban catchment, with impervious areas ranging from 94 m² to 138 ha. All sites have been instrumented so as to monitor both flow and quality at the entry of the system (or on a reference catchment when there was no centralized entry) and at its outlet. For some SCMs (VFS, ITr, ISw, BSw) this outlet consists of a drain beneath a substrate/soil layer and is representative of the water that would have been infiltrated to the underground in real situation, while for the other ones it represented the water that would have been send to sewer or directly to surface waters, either through an underground drain or a surface outlet.

This presentation focuses on a selection of micropollutants that were common to at least 2 projects: trace metals (analysed in the same lab for all 3 projects), PAHs, and 3 organic compounds (BPA, 4nonylphenol (NP) and 4 tert-octyl phenol (OP); analysed in the same lab for Roulépur and MicroMégas).

RESULTS

Runoff contamination

As expected, the contamination levels vary in a wide range from one study site to another (Figure 1). The highest pollutant concentrations were measured for the two roads with heavy traffic (Compans and Paris), while very low concentrations were measured for Coueron and Nantes. For the latter, the runoff is pretreated before its entry into the studied SCM by other SCMs (grassed swales and biofiltration swale, see Table 1), and therefore presents or very low particulate loads. Median suspended solids (SS) concentrations range from 4 mg/l to 291 mg/l between sites. Much higher Cu, Zn, OP and NP concentrations, and to a lesser extend higher PAH and BPA concentrations, are measured for the two high traffic roads. No clear relation between the scale of the catchment and the pollutant load could be drawn. The studied micropollutants and study sites differ in the distribution between dissolved and particulate phase, which has consequences on the efficiency of treatment processes. BPA was mainly found in the dissolved fraction (median particle/total <28%) while PAH were particle bound (>70%) for all sites. For Cu, Zn and NP, the proportion of particle bound pollutants varies greatly from one site to another as function of SS concentrations: >72% in median for Compans to <20% for the sites with the lowest SS. Dissolved concentrations of BPA (median up to 1100 ng/L), NP (median up to 420 ng/L, environmental quality standard EQS = 300 ng/L), and OP (median up to 400 ng/L, EQS = 100 ng/L) reach high levels on sites with heavy traffic, industrial activities or construction works.

Concentration and load reduction in SCMs

The best concentration reduction performances (Figure 1 and Figure 2) were obtained for SCMs that allow for filtration, especially those with relatively fine-graded (sandy loam or finer) vegetated soils (ISw, BSw, VFS), while those SCMs that allow only for settling (CIn, TSw, IDB, GDB, WRB) presented lower performance, or even a slight increase in concentrations when entry SS concentrations were very low. The highest concentration reduction concerned particulate pollutants. For dissolved fractions, and for contaminants with a large dissolved part (BPA, NP) performances are low, which underlines that the main processes are physical filtration and settling. Whatever the SCM, a reduction of Cu or Zn concentrations below 10 µg/L seems difficult to reach. For NP, outlet concentrations remain superior to the EQS on several sites, even after treatment. Inter-event concentration variations are attenuated at the outlet of most SCMs, which are effective in buffering extreme concentrations (Figure 1).

Load reduction performance are considerably improved, compared to concentration reductions, for those SCMs that allow for evapo(transpi)ration or infiltration (ITr, ISw, TSw, WRB). Volume reduction appears as a major factor of pollutant load control, especially for dissolved pollutants. For the BSw that allowed good concentration reductions, the global load reduction performance was however degraded by an insufficient hydraulic capacity leading to the overflow of untreated water.

CONCLUSION

Micropollutant concentration and load data measured in-situ, as a part of three French research projects, were pooled, so as to compare the performances of a wide range of stormwater control measures (SCMs). This was made possible by an exchange and harmonization working group that linked the three projects. Data acquisition is still in progress on some sites, and further data analysis and data intercomparison will continue through in the next months. One can already notice the very good performances of filtering devices for particulate load reductions, as well as the need to promote evapotranspiration in order to limit dissolved pollutant loads.

BIBLIOGRAPHIE

Fletcher, T.D., Shuster, W., Hunt, W.F., Ashley, R., Butler, D., Arthur, S., Trowsdale, S., Barraud, S., Semadeni-Davies, A., Bertrand-Krajewski, J.-L., Mikkelsen, P.S., Rivard, G., Uhl, M., Dagenais, D., Viklander, M., 2014.

SUDS, LID, BMPs, WSUD and more -The evolution and application of terminology surrounding urban drainage. Urban Water Journal 12, 525-542. Gasperi J., Sébastian C., Ruban V., Delamain M., Percot S., Wiest L., Mirande C., Caupos E., Demare D., Diallo Kessoo M., Saad M., Schwartz J.-J., Dubois P., Fratta C., Wolff H., Moilleron R., Chebbo G., Cren C., Millet M., Barraud S., Gromaire M.-C. (2014) Micropollutants in urban stormwater: occurrence, concentrations and atmospheric contribution for a wide range of contaminants on three French catchments. ESPR. 21(8), 5267-5281.

Figure 1 :

 1 Figure 1 : D10, D50 and D90 of event mean concentrations (EMCs) measured in the runoff from the different study sites (inlet in yellow and outlet in blue)

Figure 2 :

 2 Figure 2 : median EMC and event load reductions per SCM for total fraction

Table 1 :

 1 Description of study sites and SUDS : other SCMs present on the catchment, upstream of the studied SCM (Nantes: all runoff is transported by vegetated swales; Rosny: green roof and vegetated dry pond in the adjacent educational complex; Coueron: road runoff is filtered through a pervious shoulder before reaching the studied pond) # : a reference catchment is used to evaluate the micropollutant loads on similar catchments without SUDS (Lyon and Villeneuve : reference = nearby asphalt parking ; Compans : reference = nearby portion of the same road but with gutter)

	SCM type		SCM	SBV imp	α %	Catchment	Catchme
				code			type		nt name
		Pervious parking lots Infiltration trench Vegetated pervious parking Pervious concrete on a porous structure	VPa 1 PPa 1 ITr 1	1270 m² 94 m² 123 m²	100 100 21	Residential campus parking or lot	Villeneuve # Lyon #
	Source control	Swale Vegetated filter strip Infiltration swale Transportation swale TSw 1 ISw 1 Biofiltration swale BSw 1 VFS 1 Compact industrial product CIn 2	135 m² 1,3 ha 352 m² 504 m²	23 0,4 4,3 15 0	Dense residential swales High traffic road +	Nantes * Compans # Paris
		Horizontal sand filter	HSF 1	3410	1,4	Low traffic road	Rosny *
					m²	(0,6)	+	(school
					+(4186		complex)
					)
	Cen trali sed	Detentio n basin Retentio	Impervious settling pond Grassed detention pond Wet pond	IDB 2 GDB 2 WRB 2	138,7 ha 4,8 ha 8,4 ha	0,8 4,5 0,8	Industrial Road with biofiltration swale Mixed urban	Chassieu Coueron * Vertou
		n basin

1 Measured outlet = underdrain ; 2 measured outlet = surface outflow *


Development of a Guideline for Evaluating the Performance of Multi-objective Sustainable Drainage Systems (SuDS)

Le développement d'un guide méthodologique pour l'évaluation de la performance des ouvrages de maîtrise à la source des eaux pluviales K. Flanagan 1 , S. Ah-Leung 2 , L. Bacot 3 , A. Bak 4 , S. Barraud 5 , P. Branchu 6 , H. Castebrunet 5 , N. Cossais 2 , B. De Gouvello 1,7 , J.-F. Deroubaix 1 , R. Garnier 5 , M.-C. Gromaire 1 , A. Honegger 2 , P. Neveu 8 , J. Paupardin 9 , P.-E. Peyneau 10 , D. Ramier 6 , F. Rodriguez 10 , V. Ruban 10 , M. Seidl 1 , E. Thomas 11 , L. Varnede 1,6,12 1 LEESU, École des Ponts ParisTech, Champs-sur-Marne (kelsey.flanagan@enpc.fr) ; 2 EVS, ENS Lyon, Lyon ; 3 GRAIE, Villeurbanne ; 4 St Dizier Environnement, Boulogne-Billancourt ; 5 Laboratoire DEEP, INSA Lyon, Villeurbanne ; 6 Cerema, Equipe-projet TEAM, Trappes ; 7 CSTB ; 8 STEA de la Ville de Paris, Paris ; 9 Département de Seine Saint Denis, DEA, Bobigny ; 10 LEE, IFSTTAR Nantes, Bouguenais ; 11 Département de Seine et Marne, DPR, Vert Saint Denis ; 12 ECOVEGETAL, Broué RÉSUMÉ L'évaluation in situ des performances des ouvrages de maîtrise à la source des eaux pluviales pose un grand nombre de questions d'ordre méthodologique. Ainsi, dans le cadre de trois projets de recherche français dédiés à ce type d'évaluation, Matriochkas, Micromegas et Roulépur, un groupe de travail sur l'harmonisation des méthodes a été constitué afin de faciliter l'inter-comparaison des résultats issus des projets, mais aussi de rédiger un guide méthodologique à destination des acteurs opérationnels pouvant être amenés à faire ce type d'étude. Ce guide propose une démarche où la performance est évaluée pour chaque fonction de service visée pour l'ouvrage, en réponse à des enjeux locaux. La première partie du guide détaille les fonctions de service pouvant être attendues de ce type d'ouvrage. Ensuite, des indicateurs de performance sont déclinés pour une sélection de fonctions de service couramment rencontrées dans le contexte français et qui ont pu être abordées au cours des projets. Ces indicateurs se regroupent en trois catégories : les indicateurs hydrologiques (relatifs aux flux d'eau), les indicateurs pollutifs (relatifs aux polluants) et les indicateurs sociotechniques. Le guide s'appuie sur des exemples issus des trois projets pour présenter des cas pratiques de dispositifs métrologiques et d'application des indicateurs proposés.

ABSTRACT

Evaluating the performance of sustainable drainage systems (SuDS) in a field context presents a number of methodological problems. For this reason, as a part of three French research projects focused on this type of evaluation, Matriochkas, Micromegas and Roulepur, a working group on methodological harmonisation was established in order to facilitate the inter-comparison of results between the projects and propose a methodological guideline for practitioners carrying out such evaluations. The guideline proposes an approach where performance is evaluated with respect to a service function that the SuDS aims to achieve, itself identified from local issues. Its first section presents the various service functions which may be assigned to these devices. Next, performance indicators are defined for a selection of the identified service functions, common within the French context and studied as a part of the three projects. Three categories of indicators are identified: hydrologic indicators (relative to water flows), pollutant indicators and socio-technical indicators. Examples of instrumentation and of the application of the proposed indicators drawn from the experience of the three projects are also presented.

KEYWORDS

Guidelines, methodology, performance, stormwater, SuDS,

INTRODUCTION

Over the past decades, in a context combining increased urbanisation and growing concerns over the quality of the environment, urban drainage has undergone a paradigm shift. Approaches have evolved from one of rapid drainage using devices with the sole objective of evacuating stormwater, to one of onsite management using systems designed to achieve multiple objectives, known under a large number of names across the world, including sustainable drainage systems (SuDS), low impact development (LID), water sensitive urban design (WSUD), alternative techniques (techniques alternatives in French) and source control (Fletcher et al., 2014).

As these techniques are relatively recent, their performance in the complex conditions of the field context is not yet fully characterized or understood (Geberemariam, 2016). Thus, in situ performance evaluations are required in order to (i) validate that SuDS achieve the expected objectives, (ii) improve understanding of factors affecting performance and (iii) provide a basis for improving system design and optimizing performance.

Such evaluations raise a number of methodological questions. For one thing, given the multifunctional nature of these devices, performance is not a single concept but one which must be defined with respect to the objectives or functions of the system studied (Moura et al., 2011). Once the type of performance is defined, questions arise as to which performance indicators should be used to evaluate each function. The last phase is to select relevant methods for evaluating the performance indicators; this step often requires the implementation of a monitoring system, which must also be defined.

In order to harmonize methods for SuDS performance evaluation, a working group was established between three coordinated French research projects, Matriochkas, Micromegas and Roulépur, all focused on evaluating the performance of SuDS devices and financed as a part of a call for projects by the French Biodiversity Agency (AFB) and the French Water Agencies on micropollutants in urban water. The working group included both researchers and practitioners from several different institutions and served two objectives: (i) to facilitate the inter-comparison of results from the twelve sites studied as a part of the three projects and (ii) to propose a guideline for practitioners needing to carry out performance evaluations. The present article focuses on the latter objective.

METHODS

Working group organisation

The working group met regularly from the beginning of the projects in 2015 in order to discuss (i) the types of performance to be evaluated, (ii) the definition of performance indicators, (ii) the methods for evaluating indicators and, in particular, the monitoring systems to implement when measurements are required and (iv) the application of these indicators to the sites studied in the three projects.

Methodological approach

An approach was developed based on functional analysis, wherein performance is evaluated with respect to service functions intended for the device, themselves defined in response to issues within the local environmental, hydrologic, urban and political context (Figure 1).

Figure 1: Approach for evaluating performance Two types of service functions can be distinguished: usage functions, for which a device was created and constraint functions, which are constraints on the device behaviour and design given that it exists (AFNOR, 1996). Performance indicators were defined with respect to a selection of service functions, common to those observed within the French context and studied within the three research projects.

RESULTS AND DISCUSSION

Definition of issues and functions

Six issues to which sustainable drainage systems (SuDS) may respond were identified (Figure 2): flood reduction, resource preservation, ecological preservation, built environment protection, urban environmental quality and efficient management. Service functions which may be assigned to SuDS in response to each issue were identified; between two and six functions were associated with each issue, each of which was categorized as either a usage or a constraint function. Complementary or conflictual relationships exist between several service functions. When a complementary relationship exists, designing for one service function may provide benefits in terms of the other service function, even if it was not intended at the time of conception. For example, a system may be designed for volume reduction in order to limit flood risk, but volume reduction will also provide benefits in terms of pollutant load limitation. Functions may also respond to two issues; this is notably the case for pollutant load limitation which can respond to both resource and ecological preservation issues. Although the pollutants of concern are likely to be different between the two issues (for example, if the quality of a water body is to be preserved for recreational bathing, human pathogens are of greatest concern, whereas ecosystem preservation requires control of substances leading to eutrophication or ecotoxicity), designing for one of these objectives is likely to provide benefits for the other.

Conversely, when conflictual relationships exist between functions, fulfilling one function could potentially have negative effects on another function. This is the case, for example, between pollutant load limitation, which often involves retaining pollutants in the topsoil of a SuDS device, and the protection of the soil's biodegradation potential, which may be degraded if the soil is polluted. A conflict may also exist between accommodating biodiversity and pest limitation, as some species may be seen as nuisances while also contributing to biodiversity. Likewise, there may be a conflict between functions best achieved by infiltration (volume reduction, contribution to water resources) and prevention of geotechnical or hydrogeological disorders caused by infiltration. In all of these cases, there are tradeoffs between functions which require value judgements to find an optimal balance.

Issues

Service functions

Usage functions

Constraint functions

Performance indicators and monitoring

The guideline proposes performance indicators for the 17 service functions shown in red, bold text in Figure 2. Four types of indicators are identified: (i) relative indicators, which compare a value (often measured at a system outlet) to a reference corresponding to situation before or without the system; (ii) normative indicators, which compare a measured value to a level considered to be acceptable; (iii) descriptive indicators, which describe a system's behaviour, allowing for comparison with values from other systems, and (iv) explicative indicators, which seek to explain a level of performance observed.

For some functions, several indicators are proposed, which provide different types of information and may be more or less difficult to evaluate (for example, some indicators are relevant at the event time scale, others at the annual scale).

Indicators are divided into three categories: hydrologic indicators (relative to water flows or volumes), pollutant indicators (relative to pollutant loads or concentrations) and socio-technical indicators (relative to governance and / or social acceptance and use).

The collection of data necessary for the evaluation of each category of indicator is also discussed, including the identification of the system to be evaluated and the types of measurements to be carried out (flow measurement for hydrologic indicators, flow measurement and analysis of concentrations in water and/or soil for pollutant indicators and characterisation of the socio-technical system through interviews, surveys or observations of human actors for socio-technical indicators). Recommendations as to the metrology necessary to evaluate hydrologic and pollutant indicators are provided. Examples of the metrology implemented on the 12 sites studied as a part of the three projects illustrate practical difficulties associated with monitoring campaigns of SuDS devices, such as the need to choose equipment that is adapted to a site's constraints (e.g. little available space, no electrical connection) or the necessity of using a reference catchment to represent diffuse flows.

Because data collection is often costly and time-consuming, readers are encouraged to seriously consider the feasibility and relevance of the monitoring campaign (given the technical and organisational constraints and the economic, material and human resources available) before investing in the campaign. It is also acknowledged that field monitoring campaigns may not always yield all of the data expected due to unexpected constraints or data invalidation. In this case, it may be necessary to use adapted, non-ideal indicators. For example, it is generally desirable to evaluate relative indicators (for example, concentration reduction) for paired samples from the same event. However, sometimes paired samples are not obtained due to technical difficulties. In this case, distributions established over several events (or median values from these distributions) may be compared rather than paired values for each event.

CONCLUSIONS

A guideline was established to aid practitioners needing to evaluate the performance of sustainable drainage systems (SuDS) as a part of three French research projects dedicated to this goal, in parallel with monitoring campaigns at 12 different sites, enabling the practical experience derived from these projects to be taken into account. The guideline recommends first identifying the issues to which a device responds within the local context and the service functions intended to respond to these issues. Performance indicators are proposed for most of the common service functions and recommendations are made as to methods for acquiring the information required for evaluating these indicators. Once the indicators have been evaluated, the user will have at his disposal information enabling him to make an informed decision regarding the behavior and performance of the device.

Figure 2 :

 2 Figure 2: Issues to which SuDS may respond and service functions which may be expected; functions for which performance indicators are proposed are shown in bold, red text.

LIST OF REFERENCES

 AFNOR (1996). NF EN 1325-1 (Value management, value analysis, functional analysis vocabulary -Part 1: Value analysis and functional analysis). Fletcher, T.D., Shuster, W., Hunt, W.F., Ashley, R., Butler, D., Arthur, S., Trowsdale, S., Barraud, S., Semadeni-Davies, A., Bertrand-Krajewski, J.-L., Mikkelsen, P.S., Rivard, G., Uhl, M., Dagenais, D., Viklander, M. ( 2014). SUDS, LID, BMPs, WSUD and more -The evolution and application of terminology surrounding urban drainage. Urban Water J. 12(7), 525-542.

Geberemariam, T. (2016). Post Construction Green Infrastructure Performance Monitoring Parameters and Their

Functional Components. Environments 4(1), 2. Moura, P., Barraud, S., Baptista, M.B., Malard, F. (2011). Multicriteria decision-aid method to evaluate the performance of stormwater infiltration systems over the time. Water Sci. Technol. 64(10), 1993Technol. 64(10), -2000. .


Frédérique Larrarte -Ifsttar

Lhsv

Franziska Schmidt -Ifsttar

Edouard Durand -Cerema

Arnaud Bontemps -Cerema

Keywords: Structural health monitoring, scour, infrastrutures

A French experience of Structural Health Monitoring of scour affecting river infrastructures

Full Paper:

Because of their ability to connect territories and populations, any bridge failure can have a significant financial, human and social impact. As an example, the weakening of the Mayou Bridge following a flood in 2009 permanently disrupted traffic in the centre of Bayonne even though an inspection carried out two years earlier had not identified any defects/ problems. In fact, flow/structure interaction can lead to scouring process of river beds or banks that represents a significant contributing factor in the deterioration of and which can lead to their collapse during major floods. Moreover, in a rail or road transportation infrastructure system, bridge maintenance represents a high operating cost. For example, the French rail network has approximately 8,000 river crossings, of which 1,700 are potentially exposed to scouring processes. The stakes are even higher in the case of the national road network. Cofiroute, manager of approximately 10% of the French motorway network has, out of the 1,200 structures it manages, 20 viaducts under a specific monitoring programme to identify scouring problems. Across the US, 60% of reported bridge failures are due to scour of which about 20,000 bridges are identified as "scour critical" and the same number as "scour susceptible". These examples clearly show the importance and fragility of transport structures in the face of the environmental risks of floods and the importance of having observation and warning systems in place to identify disorders and their consequences in order to move towards an integrated forecasting system and integrated risk management procedures.

Financed by the French National Research Agency (ANR), the SSHEAR project, "Soils, Structures and Hydraulics: Expertise and Applied Research", comprises six partners, whose complementarity offers a major asset to the project. Specialists in soilsand in fluid mechanics; geotechnical and hydraulic engineers together with sedimentologists, physicists, infrastructure management companies and a technological research institute contribute to the project [START_REF] Chevalier | Research program SSHEAR: recent advances on the understanding and the control of scour phenomena[END_REF].

The project proposes an intensive research effort on scour erosion based on a multi-scale and multi-scientific approach using:

• physical processes of flow and erosion in the vicinity of structures (e.g. bridges, dams, embankments, quay walls),

• laboratory experiments featuring multi-scale observation,

• an innovative numerical approach built around a two-phase model,

• observations and field recordings of actual structures subjected to hydro-sedimentary forcing imposed due to environmental or anthropogenic actions.

The first step has been to identify pilot sites representative of scour vulnerability. This selection has been undertaken using the databases of SSHEAR project Partners (SNCF, Cofiroute), and validated by some field campaigns. Several criteria were defined to select the sites that would be monitored :

• bridge vulnerability to scour,

• bridge geometry (type of bridge and its representativeness, type of piers, …),

• river conditions (flow conditions, hydro-morphology, nature of sediment…),

• geology and geotechnical parameters (foundations type, bedrock or reinforcement presence…),

• site accessibility,

• staff and materials safety…

The selection has then been finalized and restricted to 3 sites:

• Site 1corresponds to the scouring of a backfill in a meander. Such situations are common in valley bottom structures, while all infrastructures are concentrated near the river, as is the case in the mountainous regions of France. This is associated with a semi mountainous climate. It has been chosen to make precise hydraulic and bathymetric surveys once a year. • Site 2 (A71road bridge over la Loire at Orléans) is representative of large structures crossing a river in France in an oceanic climate. This structure is founded on 6 piers, 4 of which are located in themain channel. It has been chosen to implement continuous monitoring devices. • Site 3(Aurence railway crossing near Limoges) is a characteristic arch bridge built on the banks of watercourses. It is also in the oceanic zone. It is representative of the structures of secondary road and rail networks. It has been chosen to implement continuous monitoring devices.

According to Breusers et al. (1977), scour can be described by equation ( 1)

dse = f(ρ, µ, U, Y, g, d, Uc, D), : (1)
where g is the acceleration of gravity; Y is the depth of water; U is the average upstream velocity; D is the diameter of the pile, ρ is the density; µ is the dynamic viscosity of the fluid, Uc is the critical value of the velocity associated with the movement of the bed particles, d is the diameter of the particles. For each measure the following items have been taken into account:

• the min-max measuring range,

• the desired characteristics (uncertainties, resolution,... • post processing (validation criteria, operation ,...)

A bibliographic review of experimetal technics have been undertaken, a table of specifications has then been sent to potential suppliers. For the two sites selected for continuous monitoring, the proposed set-ups have been developed and implemented as part of the project. On the A71 site, radar level sensor have been fixed on the bridge to measure the water level relative to a fixed point. In addition a raft made of two boards (figure 1a) is used to support a sonar instrument, used to scan the bathymetry, and a velocity profiler used to measure the velocity field. The sensors are connected to a data logger that is also sending the data to a superviser. On the Aurence site, we have implemented an aerial water level gauge, an ultrasonic velocity profiler that is mounted on a floating device in order to follow the free surface variations and a fixed drone network camera that allows us to watch the sensors periodically in order to identify any emergency situation. Due to the rural location of the site , both energy and data transmission are made by GSM (Figure 1b). a) A71 site b) Aurence site Figure 1 : set-up implemented for continuous monitoring On the Aurence site, the instrumentation has been working for 5 months and we already have feedback information. The first on is the usefulness of the camera. It has allowed the team to visualize a tree that had damaged the raft so we have been able to act quickly and repair the damaged apparatus. The second is the reactivity to the flow rate to rain events, that is also corroborating the data acquired by the French data base "Banque Hydro" (http://www.hydro.eaufrance.fr/) about 1.5 km upstream. The third reason is the importance of measuring the velocity profiles. Concerning this aspect, the first results show a hysteresis effect in relation to flowrate variations. More time is needed to analyse the hydraulic behavior in order to automatize the data processing for management purposes.

On the A71 site, the datalogger has been damaged and it has not yet been possible to recover data. However, Those two sites give a useful feedback for continuous monitoring of scour affected structures over rivers.


Nissrine Boujia
email: nissrine.boujia@ifsttar.fr

Franziska Schmidt

Christophe Chevalier

Dominique Siegert

Damien Pham Van Bang

Bridge scour monitoring technique using the vibratory response of rods embedded in the riverbed

Keywords: Bridge, Pier, Scour, Vibration, Exposed length, Equivalent cantilever, Monitoring

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Introduction

Bridge scour is the erosive action of water carrying away sediments around bridge supports, namely piers and abutments. This phenomenon accounts for nearly 60% of bridge failures in the United States [START_REF] Wardhana | Analysis of recent bridge failures in the United States[END_REF]. In France, the collapses of the Wilson Bridge in Tours (1978) and the St Louis Bridge on Reunion Island (2007) (see Fig. 1) are national examples of the damages caused by scour [START_REF] Chevalier | Scour and erosion phenomena occurring in waterwaysrecent advances (Keynote lecture)[END_REF].

In order to ensure the safety and stability of bridges, scour depth must be determined, not only during the design phase, but throughout the entire service life of the structure. To this end, on the one hand, many empirical equations were developed [START_REF] Froehlich | Analysis of onsite measurements of scour at piers[END_REF][START_REF] Melville | Pier and abutment scour: integrated approach[END_REF][START_REF] Sheppard | Live-bed local pier scour experiments[END_REF]Arneson et al., 2012;[START_REF] Sheppard | Evaluation of existing equations for local scour at bridge piers[END_REF]. However, most of these equations are derived from flume tests on small scale models and tend to either overestimate or underestimate this value. On the other hand, the traditional approach of visual inspections of the structures may not reveal the real extent of this risk since scour takes place underwater. It is therefore crucial to develop continuous monitoring techniques to anticipate future damages and collapses.

Monitoring of scour phenomenon

Indeed, in order to address this risk, various monitoring techniques have been developed. The methods based on geophysical techniques such as radar [START_REF] Gorin | Use of surface-geophysical methods to assess riverbed scour at bridge piers[END_REF][START_REF] Millard | Assessing bridge pier scour by radar[END_REF]Anderson et al, 2007) and sonar [START_REF] Deng | Bridge scour: Prediction, modeling, monitoring, and countermeasuresreview[END_REF] were largely deployed on field in early days. However, those techniques suffered from high sensitivity to noise, difficulty in the results interpretability and the impossibility to use these techniques for continuous monitoring, especially during floods [START_REF] Kong | Field Application of an Innovative Bridge Scour Monitoring System with Fiber Bragg Grating Sensors[END_REF]. For this purpose, new monitoring techniques have being proposed including the sliding magnetic collar [START_REF] Lu | Field measurements and simulation of bridge scour depth variations during floods[END_REF], time-domain reflectometry (Yankielum and Zabilansky, 1999;[START_REF] Yu | Time domain reflectometry automatic bridge scour measurement system: principles and potentials[END_REF], fiber optic [START_REF] Lin | Real-time monitoring of local scour by using fiber Bragg grating sensors[END_REF][START_REF] Zarafshan | Vibration-based method and sensor for monitoring of bridge scour[END_REF] and vibration based techniques [START_REF] Foti | Influence of foundation scour on the dynamic response of an existing bridge[END_REF][START_REF] Zarafshan | Vibration-based method and sensor for monitoring of bridge scour[END_REF][START_REF] Prendergast | An investigation of the changes in the natural frequency of a pile affected by scour[END_REF]Bao et al., 2017). Two distinct approaches have been proposed to deploy the vibration based techniques, monitoring the frequency of the bridge or the pier itself or monitoring the frequency of a rod sensor embedded around the pier. [START_REF] Foti | Influence of foundation scour on the dynamic response of an existing bridge[END_REF] studied the effect of scour on a full bridge in Italy. The response of the bridge induced by traffic was recorded before and after the retrofitting of the scoured pier. The study concluded that scour caused a decrease of the frequency and induced abnormal modal shapes of the span supported by the scoured pier. After the retrofitting, both the frequencies and modal shapes became "normal", meaning as they should be. [START_REF] Prendergast | An investigation of the changes in the natural frequency of a pile affected by scour[END_REF] investigated the feasibility of monitoring scour with an accelerometer placed on a single pile. The experimental tests were conducted using a single pile of 1.26 m pile placed in sand in the laboratory and a 8.76 m single pile on the field. His study concluded that scour causes a decrease of the first frequency, however no attempt was made to correlate the variation of the frequency to the current scour depth. [START_REF] Zarafshan | Vibration-based method and sensor for monitoring of bridge scour[END_REF] proposed to monitor scour with sensor rods. A fiber Bragg grating sensor was used to measure the frequency of the rods. In order to correlate the measured frequency to the current scour depth, a numerical model based on the Winkler theory of the soil was developed. The sensor was modeled as a beam and the soil as a series of independent linear springs. The stiffness of the springs was fixed when installing the sensor by measuring the frequency for different exposed lengths. The model was then used to identify the current scour depth: scour was modeled by the removal of the springs and the frequency of the sensor was calculated for each scour depth.

Therefore, there is a general agreement that vibration based methods can be used to detect scour, however,, some issues remain unsolved. In all the presented studies, the technique was tested in sand soil; the effect of the stiffness of the soil on the sensitivity of the frequency was not investigated. Secondly, the effect of water on the detected frequency was generally neglected. For sensor rods which are supposed to be completely immersed in water, this effect might be significant. Finally, the correlation between the current scour depth and the measured frequency in previous studies was mainly established using a numerical simulation.

The following paper tries to address the previous issues, by understanding the physical phenomena and developing a numerical model for beam-like structures embedded in soil and subjected to scour. This leads us to study the possibilities of monitoring scour with an instrumented rod embedded in the riverbed, which will call Scour-Depth Sensor (SDS) or even sensor hereafter.

First, rods of different geometries and materials were tested in the laboratory in sand at first, then in a soft clay soil to evaluate the effect of the stiffness of the soil. A numerical 3D model was then developed and validated with these tests. This numerical model was then used to compute the frequencies of the sensor completely immersed in water. Finally, based on the numerical and experimental results, a simplified cantilever model with a corrected exposed length was proposed to correlate the measured frequencies of the sensor to the current scour depth.

Laboratory validation of the scour-depth sensor

The experimental set-up

In order to investigate the effect of scour on the response of the sensor and evaluate its accuracy, extensive laboratory tests were performed. Rods of different materials, lengths and geometries were tested. Table 1 summarizes the characteristics of each rod. As shown, two lengths of the aluminum rods (L = 600 mm and L= 800 mm) were used in order to investigate the effect of the variation of the embedded length when the exposed length is kept fixed. Fig. 2 represents the circular aluminum rod. Scour was simulated by progressively increasing the exposed length of the sensor by 5 cm. For each scour depth, an impact was generated and the transient response of the rods recorded with an accelerometer placed on the top (T. Bao et al., 2017). Signal analysis, mainly Fast Fourier Transform, was then used to measure the first frequency of the rods for each scour depth.

The tests were performed in two type of soil: dry sand and a saturated clay soil. For each soil, repeatability tests were performed to evaluate the accuracy of the sensor. For each scour depth, the experiment was repeated three times in different locations of the soil. The details of the experimental tests carried out in each soil are detailed in the following sections.

Vibration tests in sand

The experimental set-up used for the test performed in sand is presented in Fig. 2. A thread is attached to the top of the rod and through a pulley; a known weight is attached to the other end. For each scour depth, the thread was cut generating an impulse force and inducing the vibration of the rod. The five rods (Table 1) were tested for different scour depths.

The results of the tests are summarized in Fig. 3. As expected, for all the tested rods, the first frequency decreases with the increase of the exposed length. The sensitivity of the rods to scour was almost the same: for a variation of the exposed length from 40 cm to 65 cm, the variation of the frequency of the rods is 47 % for the aluminum circular rods, 53% for the PVC rod and 55 % for the rectangular one. The tests showed also high repeatability of the measurement with a variability of less than 5%.The testing showed that similar rods with two different embedded lengths and the same exposed length have the same first frequency.

Vibration tests in clay soil

In order to investigate the effect of the soil characteristics on the response of the sensor, the same tests have been performed in clayey soil. A saturated clay soil was prepared by progressively mixing 50 % of sand of Fontainebleau, 50% of clay of the kaolinite clay and water. The soil was then compacted by layers of 10 cm progressively to evacuate the air contained in the soil mixture. Two changes to the previous protocol were implemented. Firstly, the method of generating the impulse force was modified: the force applied to the rod with the previous protocol led to a plastic deformation of the clay soil. Instead, a series of impacts were applied to diminish the effect of the impulse force on the properties of the soil. Secondly, tests of the circular aluminium rods showed no vibratory response. The reason why these rods do not vibrate and show only rigid body motion (translation in the Z direction, see Fig. 2, which is the direction of the impact) is that the value of their relative stiffness (EI) rod is very high compared to the stiffness of the clay soil. As so, this soil does not ensure enough constraint to the circular aluminum rods which behave as a free-free beam. The results of the rectangular aluminium rods and the circular PVC rod are summarized in Fig. 4. The tendency of the frequency of the rods in clayey soil is similar to the one in dry sand. However, the sensitivity of the rods to scour for a variation of the exposed length from 40 cm to 65 cm is lower; the variation of the frequency of the rectangular and PVC rods is 43 % and 45% respectively.

In order to better understand how the frequency of the rods varies with the stiffness of the soil they are partially embedded in, the variation of the frequency with the embedded ratio of the rods (the embedded length normalized by the total length of the rod) in sand and clay soil are plotted in Fig. 5. The embedded ratio decreases as scour develops.

The results show that for low embedded ratio, the frequency of the rods tends to be similar in both soils. However, as the embedded ratio increases, the frequency of the rod is explicitly affected by the stiffness of the soil it is embedded in.

Numerical model validation

A numerical 3D finite element model of the experimental set-up (Fig. 2) was then developed using Code-Aster software to reproduce numerically the experimental test. The material properties of the rods, namely the Young modulus and bulk density, were obtained from laboratory tests. The Young modulus of sand was derived experimentally from the Menard modulus obtained from a mini pressuremeter test (Baguelin, 1978) conducted on the block of soil used in the laboratory. The behavior of both the soil and the rod were supposed linear elastic since the vibration induced only small deformations. The accelerometer was modeled as a nodal mass at the top of the rod. In the numerical model, the rod and the soil were bounded along the interface. The lateral faces of the soil were blocked against translation in the normal direction and the base was blocked in all directions. Scour was taken into account by the extraction of a scoured layer of soil. The first frequency was obtained directly from modal analysis.

The first frequencies of the five rods were computed for each scour depth and compared to the experimental frequencies. As it can be seen from Fig. 6, the numerical results are in good agreement with the experimental results for different geometries and materials of the rods without any readjustment of the model parameters

Introduction of the presence of water

The sensor is supposed to be driven in the soil around the pier and be partially or completely submerged in the water depending on the water level. As so, the previous validated model was used to investigate the effect of water on the frequency of the sensor. For each scour depth, the exposed length of the sensor was completely immerged in water. The numerical calculation was performed using only the circular aluminum rod. The "wet" frequencies were plot against the "dry" frequencies.

As shown in Fig. 7, the "wet" frequencies of the rod are always lower. This was expected since the fluid acts as an added mass on the rod and thus decreases its frequency. The variation of frequency between the "dry" and "wet" condition was up to 10%. Therefore, for this kind of rod sensors, the effect of the fluid is not negligible and should be taken into account to accurately estimating the current scour depth.

Sensor calibration

The results of the laboratory tests in different soils detailed in Section 3 were plotted against the curve of the variation of the frequency of an equivalent cantilever. The theoretical frequencies f th of the cantilever carrying a tip mass [START_REF] Turhan | On the fundamental frequency of beams carrying a point mass: Rayleigh approximations versus exact solutions[END_REF] can be derived analytically giving Equation ( 1), where E is the Young modulus, I the inertia in the vibration direction, M the total masse of the "dry" cantilever, m the mass of the accelerometer and H the free length of the cantilever.

(

For each rod geometry and material, the frequencies of the equivalent cantilever are calculated and compared to the experimental frequencies of the rods in the soil. Figs. 8, 9 and 10 show that the experimental frequencies of the rods are translated against the theoretical frequencies of a cantilever with a fixed length H'. This means that the frequencies of the rods in the soil are identical to the frequencies of a cantilever with a free length equal to the exposed length of the rods increased with the "correction" length H'. This length varies with the rod geometry, material and the soil type. Table 2 summarizes the values of the "correction" length H', for different types of rods and soils. Since the sensor will be immersed in water which causes the decreases of the measured dry frequencies, the validity of the cantilever model has to be verified. For this propose, the calculated wet frequencies of the circular rod presented in Fig. 7 were compared to the frequency of an immersed cantilever obtained from Equation ( 2) where M a is the added mass of the fluid.

(2) Fig. 11 presents the corrected equivalent cantilever model of the circular rod in dry and wet conditions. It can be seen that when comparing the "wet" frequencies of the rod to the frequencies of "wet" cantilever model, the curves are shifted with a constant length H' wet =8cm. The cantilever model is therefore applicable in immersed condition.

Summary and conclusions

Scour is a major risk threatening the safety and stability of bridges. Determining the current scour depth is a major challenge: many previous monitoring techniques are not very efficient during floods when scour reaches its peak. The vibration technique seems to be a promising approach for a continuous monitoring of scour around piers and abutments. The reported study proposes to monitor scour by means of rods partially embedded in the riverbed. Extensive laboratory tests were performed to evaluate the effect of scour on the frequency of different sensor geometries and materials. The effect of the stiffness of the soil was also investigated: dry sand and a soft clay soil were used. The results show that the frequency is sensitive to scour in both soils, however the sensitivity of the sensor decreases with the stiffness of the soil it is embedded in. A 3D numerical model was developed and validated. It was then used to investigate the effect of the immersed condition on the frequency of the sensor. The results show that the effect of the added mass is not negligible and should be taken into account for accurate measurement of scour depth. Finally, a simplified cantilever with an increased length was proposed to correlate the exposed length of the sensor to the measured frequency and thus an estimation of the current scour depth around piers. Future research will focus on implementation of the proposed monitoring technique on field.

Anderson, N., Ismael, A., and Thitimakorn, T. (2007). Ground-penetrating radar: A tool for monitoring bridge scour. Environmental and Engineering Geoscience, 13 1-10. Arneson, L., Zevenbergen, L., Lagasse, P., and Clopper, P.(2012). Evaluating scour at bridges. Baguelin, F. (1978). The pressuremeter and foundation engineering. Trans Tech public. Bao, T., Swartz, R. A., Vitton, S., Sun, Y., Zhang, C., and Liu, Z. (2017). Critical insights for advanced bridge scour detection using the natural frequency. Journal of Sound and Vibration, 386, 116 -133.

Fig. 1

 1 Fig. 1 Collapse induced by scour of the RN1 bridge on the St Etienne River, Reunion Island (Feb 2007)

Fig. 3 Fig

 3 Fig. 3 Variation of the frequency with the exposed length in sand

Fig. 4 Fig. 5

 45 Fig. 4 Variation of the frequency with the exposed length in clay soil

  Fig. 6 Variation of the first frequency with exposed length in numerical and experimental tests

Fig. 7 Fig. 9 Fig. 10

 7910 Fig. 7 Variation of the first frequency with scour in wet and dry conditions

Fig. 11

 11 Fig. 11 Equivalent cantilever of the circular rod in dry and wet conditions

Table 1

 1 Characteristics of the rods

	Test rod	Geometry	Outer diameter/Width	Thickness	Length (mm)	Young modulus	Bulk density
			(mm)	(mm)		(GPa)	(kg/m 3 )
	Aluminum rod	Rectangular	19	2	600-800	59	2700
	Aluminum rod	Circular	12	1	600-800	59	2700
	PVC rod	Circular	20	2	800	3.5	1425

Table 2

 2 Values of the correction length of the equivalent cantilever

	Test rod	Geometry	Correction length in sand (cm)	Correction length in clay (cm)
	Aluminum rod	Rectangular	4.8	11
	Aluminum rod	Circular	8.8	Not tested
	PVC rod	Circular	4.6	11